To determine the solution to the system of equations:
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Equation 1: \( y = -2x - 6 \)
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Equation 2: \( 2y = -4x - 12 \)
We can start by simplifying the second equation. Dividing both sides of Equation 2 by 2 gives:
\[ y = -2x - 6 \]
Now we see that both equations are identical.
This means that they will intersect at an infinite number of points along the line.
Thus, the solution to the system is:
infinitely many solutions.