Download Elimination Using Multiplication Study Guide

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Elimination Using Multiplication Study Guide
Some systems of equations cannot be solved simply by adding or subtracting the
equations. A number must first multiply one or both equations before the system can be
solved by elimination. Consider the following example.
Example: Use elimination to solve the system of equations
x + 2y = 2 and 4x +5y = 5
x + 2y = 2
4x +5y = 5
Multiply –4(x + 2y = 2)
Then add the equations.
-4x – 8y = -8
4x +5y = 5
-3y = -3
y=1
Substitute 1 for y into either equation and solve for x.
x + 2(1) = 2
x+2=2
x=0
The solution of the system is (0, 1).
Use elimination to solve each system of equations.
1. 3x + 2y = 0
x – 5y = 17
2. 2x + 3y = 6
x + 2y = 5
3. 3x – y = 2
x + 2y = 3
4. 2x + 5y = 3
-x + 3y = -7
5. 2x + y = 3
-4x – 4y = -8
6. 5x – 2y = -10
3x + 6y = 66
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Use elimination to solve each system of equations.
7. 7x + 4y = -4
5x + 8y = 28
8. 4x – 2y = -14
3x – y = -8
9. 5x + 3y = -10
3x + 5y = -6
10. 2x + y = 0
5x + 3y = 2
Substitution Review: Use the substitution method to solve each system of equations.
11. y = 4x
x+y=5
12. x = -4y
3x + 2y = 20
13. y = x – 1
x+y=3
14. 3x – y = 4
2x – 3y = -9
15. 2x + 3y = 7
3x – y = 5
16. x + 6y = 2
2x + 2y = -1