Solve the following system of equations by the substitution method.

8x = 2y + 5

3x = y + 7

what is the solution set?

{(-41/2, -9/2)}
{(-9/2, -41/2)}
ø

8x = 2y + 5
3x = y + 7

We will use the second equation to substitute in the first one. Here's how to do it:
3x = y + 7
y = 3x - 7 (now substitute this in the first equation)

8x = 2y + 5
8x = 2(3x - 7) + 5
8x = 6x - 14 + 5
8x = 6x - 9
6x - 9 = 8x
6x - 8x = 9
-2x = 9
x = -9/2 (this is the first coordinate, now we need to find y)

We use the second equation again:
3x = y + 7
y + 7 = 3x
y + 7 = 3(-9/2)
y + 7 = -27/2
y = -27/2 - 7
y = -27/2 - 14/2
y = -41/2 (this is the second coordinate)

This means that the solution set is the second option: {(-9/2, -41/2)}