Question 75571
{{{3x + 3y = 9}}}
{{{y = 2x - 12}}}Plug this equation into the first one

{{{3x + 3*(highlight(2x-12)) = 9}}} Substitute 2x-12 into y
{{{3x+6x-36=9}}} Distribute the 3
{{{9x-36=9}}} Combine like terms
{{{9x=45}}}   Add 36 to both sides
{{{x=5}}}     Divide both sides by 9

Use this to find y. 
{{{3(5) + 3y = 9}}}
{{{15 + 3y = 9}}} Multiply
{{{3y = -6}}} Subtract 15 from both sides
{{{y = -2}}} Divide both sides by 3
So the solution is (5,-2)
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Check:
{{{3(5) + 3(-2) = 9}}} plug in (5,-2)
{{{-2 = 2(5) - 12}}}
{{{15 -6 = 9}}} 
{{{-2 = 10 - 12}}}
{{{9 = 9}}} works
{{{-2 = -2}}} works
So the solution satisfies the system