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Name Class 6-3 Date Enrichment Solving Systems Using Elimination Problem Solve the absolute value system of equations |x| = 2 – y x = y – 2 or x = 2 – y First isolate the absolute value expression and rewrite as a compound expression. x y2 x 2 y or 2x y 0 2x y 0 –2x + 2y = 4 2x y 0 y4 x=4 –2=2 |x|=y–2 . 2x – y = 0 Now there are two systems of linear equations to solve. Solve the first system. In first equation, add y to both sides then multiply equation by –2. Add equations. Substitute 4 for y in first equation. Solve for x. The solution for the first system is (2, 4) –2x – 2y = –4 2x y 0 3 y 4 4 y 3 x 2 4 2 3 3 Solve the second system. In first equation, add y to both sides, then multiply equation by –2. Add equations and solve for y. Substitute 4 for y in first equation. Solve for x. 3 The solution for the second system is solutions. 2 4 . Check both , 3 3 Exercises Solve each system of equations and check your answers. 2. –4y + 2x = 8 1. |x| = 3 + y x + 4y = 6 2y + 6 = |x| 4. |x – 2| + y = 2 2x + 2y = 16 3. 18y + 15 = |3x| 6y – x = 12 Prentice Hall Algebra 1 • Teaching Resources Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved. 28