Solving Systems of Equations Using Elimination
Objective: Solve systems of linear equations
using elimination
Example 1)
3 x + 2 y = 2 3 x + 2 y = 6

Add the equations 
4 y = 8 
Simplify 
y = 8/4 = 2 


Substitute using y = 2 
3 x + 2(2) = 2 

3 x + 4 = 2 
Simplify 
3 x = 2 

x = 2/3 
Solution (2/3, 2) 
Example 2)
 x  y = 8 2 x  y = 1

Subtract the equations 
x = 9 
Substitute using x = 9 
9  y = 8 

 y = 17 

y = 17 
Solution (9, 17) 
Example 3)
2 x = 3 y + 1 x + 2 y = 1

Rewrite in standard form 
2 x + 3 y = 1 x + 2 y = 1

Multiply the 2nd equation by 2 then add 
2 x + 3 y = 1 2 x  4 y = 2

Simplify 
y = 3 y = 3

Substitute using y = 3 
x + 2(3) = 1 x + 6 = 1
x = 5

Solution (5, 3) 
Example 4)
3 x + 2 y = 1 2 x  5 y = 2

Let’s eliminate the x 
2(3 x + 2 y ) = 2 (1) 3(2 x  5 y )
= 3(2)

Multiply the first equation
by 2 Multiply the 2nd equation by 3

6 x  4 y = 2 6 x  15 y = 6

Now add. 
19 y = 8 y

Now substitute 

Simplify. 

Solution: 
