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Solving Systems of Equations By Elimination Using Addition and Subtraction
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Elimination <ul><li>Elimination is the process of solving a systems of equations by eliminating one variable and solving for the other. </li></ul><ul><li>We can add two equations to eliminate one variable and solve for the other. </li></ul><ul><li>We can subtract two equations to eliminate one variable and solve for the other </li></ul>
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Elimination Using Addition The coefficients of the y terms are additive inverses, we can eliminate the y variable by adding the two equations Example
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Write the equations in column form and add The y term is eliminated Divide both sides by 4 Simplify
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Now substitute 4 for x in either equation. In this case, we will Use the second equation as it is the easier equation. Second Equation Substitute x with 4 Subtract 4 from both sides Simplify The solution is (4, 1) You can check your work by substituting the solution into the first equation
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Elimination using Subtraction Since the coefficients of the b terms are the same, we can eliminate the b -term by subtracting the two equations. Example
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Write the equation in column form And subtract The variable b is eliminated Divide each side by -4 Simplify
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Substitute c = -1 in either equation to find the value of b First equation Substitute -1 for c Simplify Add three on both sides Simplify Divide each side by 8 Reduce the fraction The solution is
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