Answer: x = 1, y = 2
Explanation:
We will solve the linear system of equations by elimination by getting opposite leading coefficients.
Given:
5x + 2y = 9
3x - 2y = -1
Multiply the top equation by 3 and the bottom by -5:
3(5x + 2y = 9)
-5(3x - 2y = -1)
-
15x + 6y = 27
-15x + 10y = 5
Add the equations together:
16y = 32
Divide both sides of the equation by 12:
y = 2
Lastly, we will substitute to solve for x:
5x + 2y = 9
5x + 2(2) = 9
Multiply:
5x + 4 = 9
Subtract 4 from both sides of the equation:
5x = 5
Divide both sides of the equation by 5:
x = 1