Download 21. Solve by Elimination

Algebra 1 Notes
Name: ____________________
Systems of Equations: Elimination Method
Example 1:
5x − 6y = −32
3x + 6y = 48
1. If you add down, the y terms will eliminate themselves.
2. Now, we can solve for the x variable.
3. We will have to substitute the value we determined for x into
one of the original equations to get the solution for the system.
Combine the solved x value and the solved y value into an ordered pair to determine the solution for the
system. ____________________.
Example 2:
5x − 2y = 3
5x + y = −9
Try these:
1.
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2x − 5y = −20
4x + 5y = 14
2.
2y = 5 − 3x
−5x + 2y = −7
Elimination with Multiplication
Sometimes, the variables will not drop out by simply adding or subtracting. If the coefficients
are different, we must ______________________ and then add or subtract to get the variables
to drop out.
Example 3:
2 x + 5 y = −22
10 x + 3 y = 22
Try These:
A.
4m + 3n = 13
2m − 4n = 1
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B.
4x + 2y = 8
5x + 6y = 3
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Example 4:
4x + 2y = 14
7x − 3y = −8
In this problem we must multiply ______ equations
by some number to make one of the variables drop
out. Would x or y be would be easier?
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Try this with a partner:
C.
3x − 4y = 10
5x + 7y = 3
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Special Cases:
1.
€
2x − y = −1
4x − 2y = 4
2.
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−2 x + y = −1
3x −1.5y = 1.5