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Explanation:
Start with the first equation. We'll plug in y = 2x+2
3x - y = 3
3x - ( y ) = 3
3x - ( 2x+2 ) = 3 ..... replace y with 2x+2
3x - 2x - 2 = 3 ..... distribute the negative through to all terms inside
x-2 = 3 ............ combine like terms
x-2+2 = 3+2 .... add 2 to both sides
x = 5
Use this x value to find the value of y. The easiest equation to use is the one in which y is already isolated for us
y = 2x+2
y = 2*5+2 ..... replace x with 5
y = 10+2
y = 12
Though we can use the other equation as well
3x-y = 3
3*5-y = 3 .... replace x with 5
15 - y = 3
15-y-15 = 3-15 ..... subtract 15 from both sides
-y = -12
y = 12 ..... multiply both sides by -1, or change the signs of both sides
We get the same result for y.
The solution is (x,y) = (5,12) meaning that the graphs of the two original equations cross at this point.
