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Estimate the solution to the system of these linear equations based on the graph. y=5x+10 y=−2x+3 (1 point)

(−1,−5) left parenthesis negative 1 comma negative 5 right parenthesis (−1, 5) left parenthesis negative 1 comma 5 right parenthesis (5,−1) left parenthesis 5 comma negative 1 right parenthesis (1, 5)

1 answer

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

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

Next, we can solve for \( x \):

  1. Add \( 2x \) to both sides: \[ 5x + 2x + 10 = 3 \] \[ 7x + 10 = 3 \]

  2. Subtract \( 10 \) from both sides: \[ 7x = 3 - 10 \] \[ 7x = -7 \]

  3. Divide by \( 7 \): \[ x = -1 \]

Now that we have \( x = -1 \), we can substitute this value back into either equation to find \( y \). Let's use the second equation:

\[ y = -2(-1) + 3 \] \[ y = 2 + 3 = 5 \]

Thus, the solution to the system of equations is \( (-1, 5) \).

Based on the options you've provided, the correct answer is: (−1, 5).