Multiply the equation:
[tex] 2x+2y=8 \mapsto 6x+6y=24 [/tex]
The solution set is the same, because multiplying both sides of an equation by a non-zero number doesn't change the solution set. In fact, if you rewrite the equation as
[tex] 2x+2y-8=0 [/tex]
Multiplying this by 3 (or whatever number, for all it matters) gives
[tex] 3(2x+2y-8)=0 [/tex]
Now, a product is zero if and only if at least one of the factor is zero. So, either [tex] 3=0 [/tex] or [tex] 2x+2y-8=0 [/tex]
Since the first is clearly impossible, the second one must be true, which is the original equation.
