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What is the solution to the system of equations graphed below?

system of y=-2x-3 and y=3x+2

Group of answer choices

(-1,1)

(-1,-1)

(0,2)

(0,-3)

1 answer

To find the solution to the system of equations given by \( y = -2x - 3 \) and \( y = 3x + 2 \), we can set the two equations equal to each other:

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

Now, we will solve for \( x \).

  1. Add \( 2x \) to both sides: \[ -3 = 5x + 2 \]

  2. Subtract \( 2 \) from both sides: \[ -5 = 5x \]

  3. Divide by \( 5 \): \[ x = -1 \]

Next, we will substitute \( x = -1 \) back into one of the original equations to find \( y \). We'll use \( y = 3x + 2 \):

\[ y = 3(-1) + 2 = -3 + 2 = -1 \]

Thus, the solution to the system of equations is:

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

Therefore, the answer is:

\((-1, -1)\)