3y = 2x-6

x + y = 8

Solve algebraically.

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.