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A system of equations is graphed on the coordinate plane.

y=−2x−4y=2x+4

What is the solution to the system of equations?

Enter the coordinates of the solution in the boxes.

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A graph of the system of equations y equals negative 2 x minus 4 and y equals 2 x plus 4.

1 answer

To find the solution to the system of equations given by:

  1. \( y = -2x - 4 \)
  2. \( y = 2x + 4 \)

we can set the two equations equal to each other since they are both equal to \( y \):

\[ -2x - 4 = 2x + 4 \]

Now, let's solve for \( x \):

  1. Add \( 2x \) to both sides:

\[ -4 = 4x + 4 \]

  1. Subtract \( 4 \) from both sides:

\[ -8 = 4x \]

  1. Divide both sides by \( 4 \):

\[ x = -2 \]

Now that we have \( x \), we can substitute it back into either of the original equations to find \( y \). Using the second equation:

\[ y = 2(-2) + 4 \]

\[ y = -4 + 4 = 0 \]

So the solution to the system of equations is:

\[ (x, y) = (-2, 0) \]

The coordinates of the solution are:

\[ \boxed{(-2, 0)} \]