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What is the solution to the system of equations below?

y = negative 2 x minus 6 and 2 y = negative 4 x minus 12
no solution
infinitely many solutions
(–3, 0)
(3, –12)

1 answer

To determine the solution to the system of equations:

  1. Equation 1: \( y = -2x - 6 \)

  2. 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.