254 Chapter 3 Systems of Linear Equations and Inequalities Example 1 Solve the system by using the addition method. Solution: 3x 4y 2 4x y 9 3x 4y 2 3x 4y 2 4x y 9 16x 4y 36 3x 4y 2 3122 4y 2 6 4y 2 4y 4 y 1 Solving a System by the Addition Method 3x 4y 2 16x 4y 36 19x 38 x 2 Multiply the second equation by 4. This makes the coefficients of the y variables opposite. Now if the equations are added, the y variable will be eliminated. Solve for x. Substitute x 2 back into one of the original equations and solve for y. Check the ordered pair (2, 1) in each original equation: 3x 4y 2 4x y 9 3122 4112 2 ✔ True 4122 112 9 ✔ True The solution set is 512, 126. Skill Practice Solve by using the addition method. 1. 2x 3y 13 x 2y 3 The steps to solve a system of linear equations in two variables by the addition method is outlined in the following box. TIP: Substituting into the other equation, 4x y 9 4122 y 9 Answer 1. {(5, 1)} produces the same value for y. 8 y 9 y 1 4x y 9, x 2 Solving a System of Linear Equations by the Addition Method Step 1 Write both equations in standard form: Ax By C . Step 2 Clear fractions or decimals (optional). Step 3 Multiply one or both equations by nonzero constants to create opposite coefficients for one of the variables. Step 4 Add the equations from step 3 to eliminate one variable. Step 5 Solve for the remaining variable. Step 6 Substitute the known value found in step 5 into one of the original equations to solve for the other variable. Step 7 Check the ordered pair in both equations and write the solution set. Avoiding Mistakes Be sure to multiply both sides of the equation by 4: 414x 92 4192 Multiply by 4.
miller_intermediate_algebra_4e_ch1_3
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