### Home > CAAC > Chapter 9 > Lesson 9.3.3 > Problem9-81

9-81.

While setting up a mathematical sentence to solve a problem, Paulina and Aliya came up with the equations below. Since the equations did not look alike, the girls turned to you for help.

Paulina: $4x+2y=6$

Aliya: $12x+6y=18$

1. Are these equations equivalent? That is, will the graph of each line be the same? Explain how you know.

What happens when you factor out the Greatest Common Factor in equation?

2. Find another equation that is equivalent to both of these. How did you find your equation?

Is there a number that you could multiply each term in the equation by that would give you an equivalent equation?