EXPLANATION
Given the system of equations:
(1) y = 2x/3 - 2
(2) y = -x +3
Substitute y= -x+3
-x + 3 = 2x/3 - 2
Isolate x for -x+3 = 2x/3 - 2
Subtract 3 from both sides:
-x + 3 - 3 = 2x/3 -2 - 3
Simplify:
-x = 2x/3 -5
Subtract 2x/3 from both sides:
-x - 2x/3 = 2x/3 - 5 -2x/3
Simplify:
-5x/3 = -5
Multiply both sides by 3:
3(-5x/3) = 3(-5)
Simplify:
-5x = -15
Divide both sides by -5
-5x/-5 = -15/-5
Simplify:
x = 3
Then, for y = -x + 3
Substitute x = 3
y = -3 + 3
Simplify:
y = 0
The solutions to the system of equations are:
y = 0 , x = 3
