If 3x-3 = xy-y and x is not =0 find the value of y.

Question

To find the value of y you must isolate the y. Let's begin by factoring both sides of the equation.

The common factor on the left is 3 and on the right it is y.

3(x-1) = y(x-1) notice that there is an (x-1) on bth sides of the equation so we can subtract (x-1) from both sides leaving. 3 = y.

Answer 1

To solve an equation for a variable, we generally isolate the variable using properties of real numbers and inverse operations. If we follow these rules we will do the following:

3x-3 = xy -y can be factored (distributive property) on both sides identifying the common factors

3(x-1) = y(x-1) 3 is the common on the left, and y is the common on the right. We get

3(x-1) /(x-1) = y by dividing (inverse of the multiplication) by (x-1) on both sides.

3 = y by simplifying on the left side under the condition that its denominator (x-1) is different than zero. Or it means that it won't be possible if x =1, where x-1 become zero (1-1=0)

The solution therefore will be y=3 for any value of x, except 1.

Answer 2

The problem has an error in the text. But that does not make it unsolvable.

If 3x - 3 = xy - y then it is correct to factor both sides of the equation.

3x - 3 is factored as 3 (x - 1)

xy - y is factored as y (x - 1)

So those values are equal. 3(x - 1) = y(x - 1)

We can DIVIDE (not subtract) both sides by x - 1 leaving 3 = y.

Let's check it by substituting 3 in place of y in the original question.

3x - 3 = xy - y

So 3x - 3 = x(3) - 3

Is this true or false. Since it is true, our solution of y = 3 is a correct one.