Answer: x = 3, y = 2
Explanation:
To use the elimination method, we will have opposite coefficients for one of the variables. Then, we will add the equations together.
Given:
2x + 3y = 12
3x + 5y = 19
Opposite coefficients:
(2x + 3y = 12) * 3
(3x + 5y = 19) * -2
Multiply:
6x + 9y = 36
-6x - 10y = -38
Add them together:
y = -2
Substitute this back into an equation and solve for x:
2x + 3y = 12
2x + 3(2) = 12
2x + 6 = 12
2x = 6
x = 3