To find the solution to the system of equations given by the graphs of \( y = 12x - 2 \) and \( y = 3x - 7 \), we need to set the two equations equal to each other since they both equal \( y \):
\[ 12x - 2 = 3x - 7 \]
Now, let's solve for \( x \):
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Subtract \( 3x \) from both sides: \[ 12x - 3x - 2 = -7 \] \[ 9x - 2 = -7 \]
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Add \( 2 \) to both sides: \[ 9x = -5 \]
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Divide by \( 9 \): \[ x = -\frac{5}{9} \]
Now, we need to find \( y \) by substituting \( x = -\frac{5}{9} \) back into either original equation. Let's use \( y = 3x - 7 \):
\[ y = 3(-\frac{5}{9}) - 7 \] \[ y = -\frac{15}{9} - 7 \] \[ y = -\frac{15}{9} - \frac{63}{9} \] \[ y = -\frac{78}{9} \] \[ y = -\frac{26}{3} \]
So the solution to the system of equations is \( x = -\frac{5}{9} \) and \( y = -\frac{26}{3} \).
However, from the choices you provided, none of the responses match this solution. If this was a multiple-choice question, it seems there might have been a mistake in the provided choices or in the problem setup.