How do you solve this equation for x and y?

Question

-3/4x+2/3y=1/2y+3

Please if you could help me step by step that would be amazing!

Answer 1

- (3 / 4)x + (2 / 3)y = (1 / 2)y + 3

As you have only one equation with two variables (x and y), you won't be able to find numerical values for x and y. You can get x in terms of y, or y in terms of x. To get numerical values you need two equations.

Multply the equation by 12 to clear all the fractions:

- 9x + 8y = 6y + 36

Collect x terms on one side, and y on the other.

Add 9x to each side:

8y = 6y + 9x + 36

Subtract 6y from each side:

2y = 9x + 36 ...(1)

Divide by 2:

y = 9x / 2 + 18.

That gives y in terms of x.

Add - 36 to each side of (1):

2y - 36 = 9x

Divide by 9:

x = 2y / 9 - 4.

That gives x in terms of y.