1. Solving Systems of Equations
So far, we have solved systems using graphing, substitution, and elimination.
This goes one step further and show how to use ELIMINATION with multiplication.
What happens when the coefficients are not the same?
We multiply the equations to make them the same! You’ll see…

2. 1) Solve the system using elimination.
2x + 2y = 6
3x – y = 5
Multiply the bottom
equation by 2
2x + 2y = 6
(2)(3x – y = 5)
2x + 2y = 6
(+) 6x – 2y = 10
8x = 16
x = 2
2(2) + 2y = 6
4 + 2y = 6
2y = 2
y = 1
(2, 1)

3. 2) Solve the system using elimination.
x + 4y = 7 4x – 3y = 9
Multiply the top equation by -4
(-4)(x + 4y = 7)
4x – 3y = 9
-4x – 16y = -28
(+) 4x – 3y = 9
-19y = -19
y = 1
4x – 3y = 9
4x – 3(1) = 9
4x – 3 = 9
4x = 12
x = 3
(3, 1)