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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  y2
x  2 y
or
2x  y  0 2x  y  0
–2x + 2y = 4
2x  y  0
y4
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
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