Algebra 1 - Solving Linear Systems by Elimination
You will learn how to solve by elimination in two different situations:
1.
One variable has opposite coefficients.
2.
One variable has coefficients that are the same.
When one variable has opposite coefficients:
Put the equations in __________________ ____________ (Ax +By = C)
Add the like terms between the two equations
One variable will cancel out
Solve for the remaining variable – substitute this answer into either original equation to find the value of the other variable.
Write the solution for each variable as an ordered pair. Check the solution in both equations.
Example 1:
4
2 x x


3
3 y y


16
8 x

_____ y

_____
Solution :( , )
******************************************************************* x

_____
Example 2:
2 x

3 y

11
 
5 y

13 y

_____
Solution :( , )

Example 3:
3 x
 
5
5 y y
 

7
14 x

_____ y

_____
Solution :( , )
******************************************************************* x

_____
Example 4:
6 x

4 y

14
 
8 y

2 y

_____
Solution :( , )

When one variable has the same coefficients:
Put the equations in standard form (Ax +By = C)
____________________ __________ _____________________ _______ ______
(change all of the signs in one of the equations) – this will make the one of the variables have opposite coefficients
Add the like terms between the two equations
One variable will cancel out
Solve for the remaining variable – substitute this answer into either original equation to find the value of the other variable.
Write the solution for each variable as an ordered pair. Check the solution in both equations.
Example 1: 
3
5 y y


2
2 x x

6
 
10 x

_____ y

_____
Solution :( , )
******************************************************************* x

_____
Example 2:
4 x

3 y

2
5 x

3 y

2 y

_____
Solution :( , )

Example 3:
2 x x y y
1
4 x

_____ y

_____
Solution :( , )
******************************************************************* x

_____
Example 4:
4 x

3 y

2
5 x

3 y
 
2 y

_____
Solution :( , )

Homework – Solving Linear Systems by Elimination
When one variable has opposite coefficients
1) x y 11
2 x y 19
2)
5 x

4 y

22

12 x

4 y
 
36
3)
4 x 2 y
 
12
4 x

8 y
 
24 x

_____ y

_____
Solution :( , ) x

_____ y

_____
Solution :( , ) x

_____ y

_____
Solution :( , )

When one variable has the same coefficients
1)
7 x

2 y

24
8 x

2 y

30
2)
 
6 y

6
6 x 3 y
 
12
3)
2 x 9 y
 
25
4 x 9 y
 
23 x

_____ y

_____
Solution :( , ) x y
Solution :( , ) x y




_____
_____
_____
_____
Solution :( , )