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Use the image to answer the question.

y = -2x + 3
y = 5x + 10
Estimate the solution to the system of these linear equations based on the graph.
y = 5x + 10
y = -2x + 3
A. (5, -1)
B. (-1, -5)
C. (1, 5)
D. (-1, 5)

1 answer

To solve for the point of intersection of the two equations \(y = -2x + 3\) and \(y = 5x + 10\), we set them equal to find \(x\):

\[ -2x + 3 = 5x + 10 \]

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

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

\[ 3 = 7x + 10 \]

  1. Subtract 10 from both sides:

\[ -7 = 7x \]

  1. Divide by 7:

\[ x = -1 \]

Now substitute \(x = -1\) back into one of the equations to find \(y\). Let's use \(y = 5x + 10\):

\[ y = 5(-1) + 10 = -5 + 10 = 5 \]

So, the point of intersection (solution to the system) is \((-1, 5)\).

Based on the choices provided, the answer is:

D. (-1, 5)