3(x+y)=y, if (x, y) is a solution to the equation above and y cannot equal to zero what is the ratio x/y

*Given
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. 
                             

The ratio, x/y in the equation, if y ≠ 0 is: x/y = -2/3.

What is the Solution of an Equation?

Solution of an equation is the value of a variable or two variables that makes an equation true.

Given:

3(x+y)=y

We are required to find the ratio, x/y if y ≠ 0.

Thus:

3(x+y)=y

Open bracket

3x + 3y = y

Subtract 3y from both sides

3x = y - 3y

3x = -2y

Divide both sides by 3

x = -2y/3

Divide both sides by y

x/y = -2/3

Therefore, the ratio, x/y in the equation, if y ≠ 0 is: x/y = -2/3.

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