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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) Responses (1, 5) left parenthesis 1 comma 5 right parenthesis (−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 answer

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

  1. \( y = 5x + 10 \)
  2. \( y = -2x + 3 \)

We need to find the point of intersection of these two equations on the graph.

  1. For the first equation: \( y = 5x + 10 \)

    • If we substitute \( x = 0 \), \( y = 5(0) + 10 = 10 \) (point \( (0, 10) \)).
    • If we substitute \( x = -1 \), \( y = 5(-1) + 10 = 5 \) (point \( (-1, 5) \)).

  2. For the second equation: \( y = -2x + 3 \)

    • If we substitute \( x = 0 \), \( y = -2(0) + 3 = 3 \) (point \( (0, 3) \)).
    • If we substitute \( x = -1 \), \( y = -2(-1) + 3 = 5 \) (point \( (-1, 5) \)).

From these calculations, we see that both equations intersect at the point \( (-1, 5) \).

Thus, the estimated solution to the system of equations is: (-1, 5)