–4x + 4y = 32
3x + 24 = 3y
If you look carefully at each equation, you will notice that each term has a common factor, which means that we can divide the equations by the appropriate factor and have an equivalent, but simpler, set of equations.
We will divide the first equation by 4 and the second equation by 3 to get:
–x + y = 8
x + 8 = y
Now let's put the first equation in the same format as the second equation.
–x + y = 8
+x +x
y = x + 8
x + 8 = y
What do you know? These lines are identical!!! The two original equations are just two different ways of expressing the same line. You could say there are an infinite number of solutions, or points on the line, though not every point, of course, is on the line.
