WebThe moment of inertia, otherwise known as the mass moment of inertia, angular mass, second moment of mass, or most accurately, rotational inertia, of a rigid body is a quantity that determines the torque needed for a desired angular acceleration about a rotational axis, akin to how mass determines the force needed for a desired acceleration.It depends on 30. The values of r and s are equidistant from the center by an unknown quantity u. Practice your math skills and learn step by step with our math solver. \left(-\frac{1}{\sin(\theta )}\right)\times \left(\frac{\cos(\theta )}{\sin(\theta )}\right). To add polynomials, always add the like terms, i.e. Substitute the value of u to compute the r and s. Factor out x in the first and 5 in the second group. so that the highest point the object can reach is 300 feet above ground. Rewrite x^{2}+4x-5 as \left(x^{2}-x\right)+\left(5x-5\right). Quadratic polynomial can be factored using the transformation ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right), where x_{1} and x_{2} are the solutions of the quadratic equation ax^{2}+bx+c=0. Move the terms of the $y$ variable to the left side, and the terms of the $x$ variable to the right side of the equality, Integrate both sides of the differential equation, the left side with respect to $y$, and the right side with respect to $x$, The integral of a constant is equal to the constant times the integral's variable, Solve the integral $\int1dy$ and replace the result in the differential equation, We can solve the integral $\int\sin\left(5x\right)dx$ by applying integration by substitution method (also called U-Substitution). https://www.tiger-algebra.com/drill/x~3-8x~2_12x=0/, https://www.tiger-algebra.com/drill/x~3-8x~2_17x-6/, http://www.tiger-algebra.com/drill/x~3-8x~2-x_8=0/, https://www.tiger-algebra.com/drill/x~5-2x~3-x~2_2/, https://www.tiger-algebra.com/drill/x~5-4x~3-x~2_4/, https://www.tiger-algebra.com/drill/x~5-9x~3-x~2_9/, x^{3}\left(x^{2}-1\right)-8\left(x^{2}-1\right). 2022 Leaf Group Ltd. / Leaf Group Media, All Rights Reserved. WebRsidence officielle des rois de France, le chteau de Versailles et ses jardins comptent parmi les plus illustres monuments du patrimoine mondial et constituent la plus complte ralisation de lart franais du XVIIe sicle. Find Vertex and Intercepts of Quadratic Functions - Calculator: Solver to Analyze and Graph a Quadratic Function. As it happens, any equation that can appear as: where A, B and C are constants, x is the independent variable and y is the dependent variable is a linear equation. Whether you need help solving quadratic equations, inspiration for the upcoming science fair or the latest update on a major storm, Sciencing is here to help. (5s2+2s+1). We will use a new variable y = x(20p + x). m is the slope, or tilt, of the line on the graph, whereas b is the y-intercept, or the point (0. We will guide you on how to place your essay help, proofreading and editing your draft fixing the grammar, spelling, or formatting of your paper easily and cheaply. The profit (in thousands of dollars) of a company is given by. x=\frac{-4\sqrt{4^{2}-4\left(-5\right)}}{2}. WebIt can do almost any integral that can be done in terms of standard Rewrite Triple Integral Calculator. To use the direct factoring method, the equation must be in the form x^2+Bx+C=0. Web- Rewrite Y is equal to 2/3x plus 4/7 in standard form. 3. Our math solver supports basic math, pre-algebra, algebra, trigonometry, calculus and more. WebSolve Exponential Equations for Exponents using X = log(B) / log(A). y) at which the the line crosses the y, or vertical, axis. Due to the fact that x and y are different variables, this expression cannot be simplified. Write the polynomial in descending order. To find linear differential equations solution, we have to derive the general form or representation of the solution. Let y = U x. If you would like to change your settings or withdraw consent at any time, the link to do so is in our privacy policy accessible from our home page. Variables are also sometimes called indeterminates. Math Questions With Answers (13): Quadratic Functions. Add -4 to 6. Access detailed step by step solutions to thousands of problems, growing every day! Polynomial x^{2}+2x+4 is not factored since it does not have any rational roots. Kevin Beck holds a bachelor's degree in physics with minors in math and chemistry from the University of Vermont. Our goal is to make science relevant and fun for everyone. WebAlgebra with pizzazz worksheet answers 101, quadratic equation extremum, algebra like terms worksheets, how to work out 2004 maths sats paper KS3, Kumon work sheets, "free online algebra calculator". Non-Linear Differential Equation Ti-89 dirac delta function, solving literal equations worksheet, multiplying and simplifying calculator, Help with KS3 maths algebra negative numbers. About the Author. the graph of a quadratic function written in the form, at the point (h , k) where h and k are given by, + b x + c = 0 has one solution and the graph of f(x) = a x, + b x + c = 0 has two real solutions and the graph of f(x) = a x, + b x + c = 0 has two complex solutions and the graph of f(x) = a x. where x is the amount ( in thousands of dollars) the company spends on advertising. f(x) = x 2 + x + c If x^2 or y^2 terms appear, try to collect them on one side of the equation. Put your understanding of this concept to test by answering a few MCQs. WebThis will yield the equation (LU)x = b. The factors r and s are the solutions to the quadratic equation. For example, 3x, A standard polynomial is the one where the highest degree is the first term, and subsequently, the other terms come. Solution to Problem 5, Problem 6 Check out all of our online calculators here! Example: 2 To simplify an expression $$4x^2 + 3x + 4y + 8x + 9x^2$$. The degree of zero polynomial is not defined while the degree of a constant polynomial is 1. You can also see that the midpoint of r and s corresponds to the axis of symmetry of the parabola represented by the quadratic equation y=x^2+Bx+C. The values of r and s are equidistant from the center by an unknown quantity u. The formula y = mx + b is an algebra classic. WebA differential equation in which the degrees of all the terms is the same is known as a homogenous differential equation. If you already have an equation in this form, finding b is trivial. denotes the factorial of n.In the more compact sigma notation, this can be written as = ()! "Sinc Identify the values of a, b, Quadratic Equation Calculator Input MUST have the format: AX 2 + BX + C = 0 EXAMPLE Standard Form: Ax + By = C. This means that we want the variables (x & y) to be on the left-hand side and the constant (6) to be on the right-hand side. WebWhen written in "vertex form ": (h, k) is the vertex of the parabola, and x = h is the axis of symmetry. WebAlso, the differential equation of the form, dy/dx + Py = Q, is a first-order linear differential equation where P and Q are either constants or functions of y (independent variable) only. Now subtract it and bring down the next term. Will calculate the value of the exponent. Find the slope and y-intercept of 2x - 3y = 6. the h represents a horizontal shift (how far left, or right, the graph has shifted from x = 0). If the linear equation is given in the form y = m * x + b, just set x to zero and solve. var cid='7714110523';var pid='ca-pub-8886524782132322';var slotId='div-gpt-ad-analyzemath_com-medrectangle-3-0';var ffid=1;var alS=1021%1000;var container=document.getElementById(slotId);container.style.width='100%';var ins=document.createElement('ins');ins.id=slotId+'-asloaded';ins.className='adsbygoogle ezasloaded';ins.dataset.adClient=pid;ins.dataset.adChannel=cid;if(ffid==2){ins.dataset.fullWidthResponsive='true';} The values of r and s are equidistant from the center by an unknown quantity u. You can also see that the midpoint of r and s corresponds to the axis of symmetry of the parabola represented by the quadratic equation y=x^2+Bx+C. Repeat steps 2 to 4 until you have no more terms to carry down. Factor out common term x^{2}-1 by using distributive property. We can perform arithmetic operations such as addition, subtraction, multiplication, and also positive integer exponents for polynomial expressions but not division by variable. Prop 30 is supported by a coalition including CalFire Firefighters, the American Lung Association, environmental organizations, electrical workers and businesses that want to improve Californias air quality by fighting and preventing wildfires and reducing air pollution from vehicles. WebDefinition. Solution We first solve for y in terms of x by adding -2x to each member. The differential equation in first-order can also be written as; https://www.tiger-algebra.com/drill/x~2_4x-5/, https://socratic.org/questions/how-do-you-write-2x-2-4x-5-into-vertex-form, https://socratic.org/questions/how-do-you-evaluate-the-limit-3x-2-4x-5-as-x-approaches-5, https://socratic.org/questions/what-must-be-added-to-3x-7-to-make-it-x-2-4x-1, https://www.tiger-algebra.com/drill/x~2_4x-2/, https://www.tiger-algebra.com/drill/x~2_4x-3/. Rewrite the complete factored expression. Find the coefficients a,b and c. Solution to Example 1. and the graph of the line whose equation is given by. WebDifferential Equation Definition. Alright, we'll worry about this second part in a little bit. a) 2 points of intersection, We and our partners use cookies to Store and/or access information on a device.We and our partners use data for Personalised ads and content, ad and content measurement, audience insights and product development.An example of data being processed may be a unique identifier stored in a cookie. Note: 20p + x is simply twice If the linear equation is given in the form y = m * x + b, just set x to zero and solve. dy/dx = f(x) Here x is an independent variable and y is a dependent variable. Webhas a slope 1/4 and a y-intercept -2. In this example, there are three terms: x, The word polynomial is derived from the Greek words poly means . The only such pair is the system solution. WebSolve your math problems using our free math solver with step-by-step solutions. Manage SettingsContinue with Recommended Cookies. Therefore, division of these polynomial do not result in a Polynomial. The quadratic formula gives two solutions, one when is addition and one when it is subtraction. WebA first-order differential equation is defined by an equation: dy/dx =f (x,y) of two variables x and y with its function f(x,y) defined on a region in the xy-plane.It has only the first derivative dy/dx so that the equation is of the first order and no higher-order derivatives exist. So it's Y is equal to 2/3x plus 4/7. have: Following a bumpy launch week that saw frequent server trouble and bloated player queues, Blizzard has announced that over 25 million Overwatch 2 players have logged on in its first 10 days. if(typeof ez_ad_units!='undefined'){ez_ad_units.push([[580,400],'analyzemath_com-banner-1','ezslot_8',360,'0','0'])};__ez_fad_position('div-gpt-ad-analyzemath_com-banner-1-0'); Problem 3 To view the purposes they believe they have legitimate interest for, or to object to this data processing use the vendor list link below. b) 1 point of intersection, Find values of the parameter c so that the graphs of the quadratic function f given by , .., x and constant term respectively and it should belong to real number ( R). Check out all of our online calculators here! Click Start Quiz to begin! Kevin Beck holds a bachelor's degree in physics with minors in math and chemistry from the University of Vermont. Since ab is negative, a and b have the opposite signs. Find the equation of the quadratic function f whose graph passes through the point (2 , -8) and has x intercepts at (1 , 0) and (-2 , 0). \left(-\csc(\theta )\right)\times \left(\frac{\cos(\theta )}{\sin(\theta )}\right). The y-intercept, b is therefore 7. notice that the h value is subtracted in this form, and that the k value is added. The values of r and s are equidistant from the center by an unknown quantity u. WebThis means the variable terms are not squared (such as x^2 or y^2) or some higher power. Solution to Example 1. WebDifferential Equations Calculator Get detailed solutions to your math problems with our Differential Equations step-by-step calculator. 2022. () +,where n! The derivative of the constant 1 is 0, and the derivative of sin(\theta ) is cos(\theta ). Rewrite x^{2}-1 as x^{2}-1^{2}. But sometimes, a few steps are required to get there. Our math solver supports basic math, pre-algebra, algebra, trigonometry, calculus and more. Factor out common term x-1 by using distributive property. 3. Also, register now to access numerous video lessons for different math concepts to learn in a more effective and engaging way. 30. is for ease of graphing. Step 1: Divide All Terms in the Equation by B. WebTo find the coordinates of the point of intersections of the graphs of f(x) = x 2 + x + c and y = 2 x, we need to solve the system y = x 2 + x + c and y = 2 x which by substitution , gives the equation x 2 + x + c = 2x Rewrite the above equation in standard form x 2 - x + c = 0 Find the discriminant D D = 1 - 4 c 2022. WebSolve your math problems using our free math solver with step-by-step solutions. The equation must be simplified, which means all numbers must be integers that do not share a common factor other than one. x=\frac{-4\sqrt{16-4\left(-5\right)}}{2}. Then solve the equation L y = b for y. 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Solution to Problem 3, Problem 4 (),where f (n) (a) denotes the n th derivative of f evaluated at the point a. Do the grouping x^{5}-x^{3}-8x^{2}+8=\left(x^{5}-x^{3}\right)+\left(-8x^{2}+8\right), and factor out x^{3} in the first and -8 in the second group. Now solve the equation x=\frac{-46}{2} when is plus. +x-12. () + ()! We need to calculate $du$, we can do that by deriving the equation above, Substituting $u$ and $dx$ in the integral and simplify, Take the constant $\frac{1}{5}$ out of the integral, Apply the integral of the sine function: $\int\sin(x)dx=-\cos(x)$, Replace $u$ with the value that we assigned to it in the beginning: $5x$, Solve the integral $\int\sin\left(5x\right)dx$ and replace the result in the differential equation, As the integral that we are solving is an indefinite integral, when we finish integrating we must add the constant of integration $C$. C(x) has a minimum value of 120 thousands for x = 2000 and the fixed cost is equal to 200 thousands. Some of our partners may process your data as a part of their legitimate business interest without asking for consent. Find the equation of the tangent line to the the graph of f(x) = - x 2 + x - 2 at x = 1. Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). WebQuadratic equation calculator shows work, equation of elipse, grade 10 factors help, triginometry calculator, lcm excel formula, softmath, java input in bold. Problem 2 Enter the non negative of the quadrant of a circle can be calculated by the method of integration used for calculating area under the curve.The equation of the curve is y = (a 2 - x 2) and the limit is from O to a. Subtract 6 from -4. x^{2}+4x-5=\left(x-1\right)\left(x-\left(-5\right)\right). Determine the greatest digit x such that (+). 4.. An online LU matrix decomposition calculator is included and may be used to check the solutions and answers below. Solution to Problem 6. Since a+b is positive, the positive number has greater absolute value than the negative. For example, x. Check the highest power and divide the terms by the same. Required fields are marked *, A polynomial is an expression that consists of variables (or indeterminate), terms, exponents and constants. WebFind p, y and x, as follows: Let p be the part of the root found so far, ignoring any decimal point. WebIntegrals by Partial Fraction expansion Calculator Get detailed solutions to your math problems with our Integrals by Partial Fraction expansion step-by-step calculator. Examples with Solutions Example 1 Find the L U composition of matrix A = [ 1 1 2 1] . The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right). Keep visiting BYJUS to get more such math lessons on different topics. Express r and s with respect to variable u. -\frac{\cos(\theta )}{\left(\sin(\theta )\right)^{2}}. Your Mobile number and Email id will not be published. 6. WebExample: 1 Consider the expression: $$4x + y.$$. Free online calculators for exponents, math, fractions, factoring, plane geometry, solid geometry, algebra, finance and more. WebTwo numbers r and s sum up to -4 exactly when the average of the two numbers is \frac{1}{2}*-4 = -2. Let me get my scratch pad out. You can also see that the midpoint of r and s corresponds to the axis of symmetry of the parabola represented by the quadratic equation y=x^2+Bx+C. Consider x^{2}-1. It is possible to solve equations with x^2 and y^2 terms by the same methods we have used so far. Find values of the parameter m so that the graph of the quadratic function f given by, Problem 5 , To solve for unknown quantity u, substitute these in the product equation rs = -5, Simplify by expanding (a -b) (a + b) = a^2 b^2, Simplify the expression by subtracting 4 on both sides, Simplify the expression by multiplying -1 on both sides and take the square root to obtain the value of unknown variable u. You can also see that the midpoint of r and s corresponds to the axis of symmetry of the parabola represented by the quadratic equation y=x^2+Bx+C. It represents a linear equation, the graph of which, as the name suggests, is a straight line on the x-, y-coordinate system. WebTwo-step equation calculator, 7th grade algebra help, linear equation java code, missing ordinal numbers worksheet, algebra help AND world problems, free online math problem solver for 3 graders. The quadratic function C(x) = a x 2 + b x + c represents the cost, in thousands of Dollars, of producing x items. therefore I wanna some help, Its good it helped me very much for my project, Your Mobile number and Email id will not be published. For example, in: All terms are in the proper place and form, because y has a coefficient of 1. A differential equation is an equation which contains one or more terms and the derivatives of one variable (i.e., dependent variable) with respect to the other variable (i.e., independent variable). First, we must identify a section within the integral with a new variable (let's call it $u$), which when substituted makes the integral easier. Let r and s be the factors for the quadratic equation such that x^2+Bx+C=(xr)(xs) where sum of factors (r+s)=B and the product of factors rs = C, Two numbers r and s sum up to -4 exactly when the average of the two numbers is \frac{1}{2}*-4 = -2. First, the expression needs to be rewritten as x^{2}+ax+bx-5. WebThe moment of inertia, otherwise known as the mass moment of inertia, angular mass, second moment of mass, or most accurately, rotational inertia, of a rigid body is a quantity that determines the torque needed for a desired angular acceleration about a rotational axis, akin to how mass determines the force needed for a desired acceleration.It depends on WebStandards Documents High School Mathematics Standards; Coordinate Algebra and Algebra I Crosswalk; Analytic Geometry and Geometry Crosswalk; New Mathematics Course \left(x-2\right)\left(x-1\right)\left(x+1\right)\left(x^{2}+2x+4\right). Example 3 . Quadratic equations such as this one can be solved by a new direct factoring method that does not require guess work. The addition of polynomials always results in a polynomial of the same degree. WebSolve your math problems using our free math solver with step-by-step solutions. Note the final answer, including remainder, will be in the fraction form (last subtract term). WebWe would like to show you a description here but the site wont allow us. WebTwo numbers r and s sum up to -2 exactly when the average of the two numbers is \frac{1}{2}*-2 = -1. WebThis will yield the equation (LU)x = b. Group the terms of the differential equation. Let's define a variable $u$ and assign it to the choosen part, Now, in order to rewrite $dx$ in terms of $du$, we need to find the derivative of $u$. WebFast Company is the world's leading progressive business media brand, with a unique editorial focus on innovation in technology, leadership, and design. Let's see if we can rewrite this. The Taylor series of a real or complex-valued function f (x) that is infinitely differentiable at a real or complex number a is the power series + ()! More about Kevin and links to his professional work can be found at www.kemibe.com. A = 4 Oa y.dx. WebTwo numbers r and s sum up to -7 exactly when the average of the two numbers is \frac{1}{2}*-7 = -\frac{7}{2}. For example, dy/dx = 5x An object is thrown vertically upward with an initial velocity of Vo feet/sec. $\left(1+x^4\right)\cdot dy+x\cdot\left(1+4y^2\right)\cdot dx=0$, $\frac{dy}{dx}=\frac{3x^2+4x+2}{2\left(y+1\right)}$. Use the answer in step 2 as the division symbol. y + x(dy/dx) = 0 is a homogenous differential equation of degree 1. x 4 + y 4 (dy/dx) = 0 is a homogenous differential equation of degree 4. Substitute 1 for x_{1} and -5 for x_{2}. Rewrite the quotient as a product of two quotients. WebAbout Our Coalition. Factor the expression by grouping. WebPolynomials are algebraic expressions that consist of variables and coefficients. ins.style.display='block';ins.style.minWidth=container.attributes.ezaw.value+'px';ins.style.width='100%';ins.style.height=container.attributes.ezah.value+'px';container.appendChild(ins);(adsbygoogle=window.adsbygoogle||[]).push({});window.ezoSTPixelAdd(slotId,'stat_source_id',44);window.ezoSTPixelAdd(slotId,'adsensetype',1);var lo=new MutationObserver(window.ezaslEvent);lo.observe(document.getElementById(slotId+'-asloaded'),{attributes:true}); If a > 0, the vertex is a minimum point and the minimum value of the quadratic function f is equal to k. This minimum value occurs at x = h. 6. x 2 + y 2 xy and xy + yx are examples of homogenous differential equations. https://math.stackexchange.com/questions/1984114/on-a-polynomial-with-roots-in-1-3-that-are-also-of-the-form-2-csc-theta, https://socratic.org/questions/56e382a47c014915a4b08b44, https://math.stackexchange.com/questions/1477117/determine-the-exact-value-of-sin-theta-cos-theta-if-csc-theta-3, https://socratic.org/questions/how-do-you-find-the-values-of-the-six-trigonometric-functions-given-csctheta-4-a, https://socratic.org/questions/how-do-you-use-csctheta-5-to-find-cottheta, https://math.stackexchange.com/questions/1189707/how-to-explain-that-int-frac-sec-theta-tan2-thetad-theta-is-equal-to, \frac{\mathrm{d}}{\mathrm{d}\theta }(\frac{1}{\sin(\theta )}), \frac{\sin(\theta )\frac{\mathrm{d}}{\mathrm{d}\theta }(1)-\frac{\mathrm{d}}{\mathrm{d}\theta }(\sin(\theta ))}{\left(\sin(\theta )\right)^{2}}. The difference of cubes can be factored using the rule: a^{3}-b^{3}=\left(a-b\right)\left(a^{2}+ab+b^{2}\right). The slope b in this instance is simply 7. () + ()! WebGet breaking NBA Basketball News, our in-depth expert analysis, latest rumors and follow your favorite sports, leagues and teams with our live updates. $\exponential{x}{5} - \exponential{x}{3} - 8 \exponential{x}{2} + 8 $. The quadratic function f(x) = a x 2 + b x + c can be written in vertex form as follows: if(typeof ez_ad_units!='undefined'){ez_ad_units.push([[580,400],'analyzemath_com-box-4','ezslot_5',260,'0','0'])};__ez_fad_position('div-gpt-ad-analyzemath_com-box-4-0'); Problem 1 Let y = U x. Practice your math skills and learn step by step with our math solver. Rewrite y = 2x - 6 in standard form. Simplify all the expressions of the form p-\left(-q\right) to p+q. Then solve the equation L y = b for y. WebGet 247 customer support help when you place a homework help service order with us. For any two differentiable functions, the derivative of the quotient of two functions is the denominator times the derivative of the numerator minus the numerator times the derivative of the denominator, all divided by the denominator squared. Select the correct answer and click on the Finish buttonCheck your score and answers at the end of the quiz, Visit BYJUS for all Maths related queries and study materials, I am doing algebra at school , and I forgot alot about it. (For the first step, p = 0.) Microsoft pleaded for its deal on the day of the Phase 2 decision last month, but now the gloves are well and truly off. Solve the equation using the Quadratic Formula. Note that B here is not the same as b above. Calculator simple exponents and fractional exponents Consider x^{3}-8. and the graph of the line whose equation is given by y = 2 x Rewriting Equations in Standard Form. Its distance S(t), in feet, above ground is given by. If a < 0, the vertex is a maximum point and the maximum value of the quadratic function f is equal to k. This maximum value occurs at x = h. Formerly with ScienceBlogs.com and the editor of "Run Strong," he has written for Runner's World, Men's Fitness, Competitor, and a variety of other publications. WebThe height is defined in terms of the width, so I'll pick a variable for "width", b 60, and c 147. t So, t. 3.39 or t. This is a quadratic equation, rewrite it in standard form. Rewrite x^{3}-8 as x^{3}-2^{3}. the terms having the same variable and power. We see that $5x$ it's a good candidate for substitution. the k represents a vertical shift (how far up, or down, the graph has shifted from y = 0). c) no points of intersection. x^{2}+4x-5=\left(x-1\right)\left(x+5\right). All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b\sqrt{b^{2}-4ac}}{2a}. If an equation is not written in x = mx + b form and we want to know the slope and/or the y-intercept, we rewrite the equation by solving for y in terms of x. Examples with Solutions Example 1 Find the L U composition of matrix A = [ 1 1 2 1] . Say you have an equation: This reduces the coefficient of y to 1, as desired. Solution: Collect and add the like terms which gives; $$9x^2 + 4x^2+ 8x + 3x + 4y => 13x^2 + 11x + 4y.$$ Based on this example, we can conclude that Webwithout solving the equation or factoring, determine the solution to the equation -9, using only the graph ; ti 89 complete square ; Holt, Rinehart and Winston worksheet answers for Skills worksheet section: Scientific Methods ; multiplying integers with parenthesis ; slope and y-intercept calculator ; slope intercept form solving on ti-84 Often, however, an equation that can ultimately be represented in this form appears in disguise. 4.. An online LU matrix decomposition calculator is included and may be used to check the solutions and answers below. An example of a polynomial with one variable is The consent submitted will only be used for data processing originating from this website. This cannot be simplified. Our math solver supports basic math, pre-algebra, algebra, trigonometry, calculus and more. \frac{6x - 3y}{3} = \frac{21}{3} \\ \,\\ 2x - y = 7, -y = 7 + 2x \\ y = -7 - 2x \\ y = -2x -7 \\, 6x -3y = 21 \\ (6 0) - (3 -7) = 21 \\ 0 + 21 = 21, MathCentral: Converting y=mx+b into ax+by+c=0 and Vice Versa, Math: Basic Equations of Lines and Planes. Now solve the equation x=\frac{-46}{2} when is minus. To find a and b, set up a system to be solved. 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