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Algebra I –Wilsen
Unit 6: Systems of Equations
Day Five
BLOCK 2
Solving Systems of Equations: Elimination
We have already learned to solve systems of equations using substitution. Now we will
learn to solve them using ELIMINATION.
To solve a system of equations using elimination, follow these steps:
Step 1:
Add the equations together so that either the x’s or the y’s are eliminated (that
is, they cancel out).
Step 2:
Solve the resulting equation for x or y, whichever still exists.
Step 3:
Substitute to find the value of the other variable.
________________________________________________________________________
Example 1:
x + y = 19
x–y =9
The final solution is x = ____, y = ____
Example 2:
3x + 2y = 7
–3x + y = –1
The final solution is x = ____, y = ____
Step 1:
If the x’s or y’s won’t cross out, multiply an entire equation by a number to get
either x's or y's to match.
Step 2:
Add the equations together so that either the x’s or the y’s are eliminated (that
is, they cancel out).
Step 4:
Solve the resulting equation for x or y, whichever still exists.
Step 5: Substitute to find the value of the other variable.
________________________________________________________________________
Example 3:
–2x + 5y = 11
x + 2y = 8
The final solution is x = ____, y = ____
________________________________________________________________________
Example 4:
2x + y = –2
–3x + 4y = 14
The final solution is x = ____, y = ____
Solve each of the following systems of equations using the elimination method.
Remember, you can check your answers!!
1.
2x + y = 3
3x – y = –8
x = __________
y = __________
2.
x + 3y = –3
–x + y = –5
x = __________
y = __________
3.
x + 2y = 17
3x – 2y = 11
x = __________
y = __________
4.
2x + 2y = 18
3x – 2y = –8
x = __________
y = __________
5.
x + 5y = –14
–x + 2y = –7
x = __________
y = __________
6.
x + 2y = –4
6x – 2y = –38
x = __________
y = __________