Question

Use substitution to solve each system of equations. If the system does not have exactly one solution, state whether it has no solution or infinitely many solutions.

3x - 2y = 11

x - y/2 = 4

Answer 1

x - y/2 = 4
x - 4 = y/2
2(x - 4) = y
2x - 8 = y.....so we sub in 2x - 8 in for y in the other equation

3x - 2y = 11
3x - 2(2x - 8) = 11
3x - 4x + 16 = 11
-x = 11 - 16
-x = -5
x = 5

2x - 8 = y
2(5) - 8 = y
10 - 8 = y
2 = y

It has one solution and it is (5,2)