3(x+y)=y If (x, y) is a solution to the equation above and y does not equal 0, what is the ratio x/y?

please add an explanation.

3(x+y)=y

y is not equal to zero

*Solution  

1. The given equation is 3(x+y) = y and we are tasked to find the ratio between x and y. Distributing 3 to the terms in the parenthesis,  

                       3(x+y) = y

                     3x + 3y = y

Transposing 3y to the right side OR subtracting 3y from both the left-hand side and the right-hand side of the equation would give

                             3x = -2y

Dividing both sides of the equation by 3,  

                               x = (-2/3)y

Dividing both sides of the equation by y,  

                             x/y = -2/3

Therefore, the ratio x/y has a value of -2/3 provided that y is not equal to zero.