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The system of equations is graphed on the coordinate plane.

y=−x−2y=3x+2

Enter the coordinates of the solution to the system of equations in the boxes.

1 answer

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

  1. \( y = -x - 2 \)
  2. \( y = 3x + 2 \)

we can set them equal to each other since they both equal \( y \):

\[ -x - 2 = 3x + 2 \]

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

  1. Add \( x \) to both sides: \[ -2 = 4x + 2 \]

  2. Subtract \( 2 \) from both sides: \[ -4 = 4x \]

  3. Divide by \( 4 \): \[ x = -1 \]

Now that we have \( x = -1 \), we can substitute it back into either equation to find \( y \). We'll use the first equation:

\[ y = -(-1) - 2 = 1 - 2 = -1 \]

Thus, the coordinates of the solution to the system of equations are:

\[ (x, y) = (-1, -1) \]

Therefore, the answer is: \[ \text{Coordinates: } (-1, -1) \]