Answer:
Choice C) no solutions
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Work Shown:
y+7 = 3x turns into y = 3x-7 after we subtract 7 from both sides
Plug that into the other equation and solve for x
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6x - 2y = 12
6x - 2( y ) = 12
6x - 2( 3x-7 ) = 12 ... y replaced with 3x-7
6x - 2(3x) - 2(-7) = 12
6x - 6x + 14 = 12
0x + 14 = 12
0 + 14 = 12
14 = 12 ... this is a contradiction, aka false statement
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No matter what x value we pick, the equation above will always be false.
Therefore, there are no solutions
We say that this system of equations is inconsistent.
Graphing both equations leads to two parallel lines. A solution only happens if the lines cross, but parallel lines never intersect.