3y = 2x - 6 Solve one equation for a variable. I'll solve the second one for x + y = 8 y.
x + y = 8 Subtract x from both sides
y = 8 - x
Now, substitute this y value (8 - x) into the other given equation and solve for x.
3y = 2x - 6 Replace y with 8 - x
3(8 - x) = 2x - 6 Multiply 3 (8 - x)
24 - 3x = 2x - 6 Add 3x to both sides
24 = 5x - 6 Add 6 to both sides
30 = 5x Divide both sides by 5
6 = x Flip the equation to make it easier to read
x = 6
Now, use the x + y = 8 equation, replace the x with 6, and solve for y.
x + y = 8 Substitute x for 6
6 + y = 8 Subtract 6 from both sides
y = 2
Check your answers in both equations.
3y = 2x - 6 Replace x and y with 6 and 2
3(2) = 2(6) - 6 Simplify 3(2)
6 = 2(6) - 6 Simplify 2(6)
6 = 12 - 6 Subtract
6 = 6
x + y = 8 Replace x and y with 6 and 2
6 + 2 = 8 Add
8 = 8
So, the answers to your system of equations are x = 6 and y = 2 .