Question

Estimate the solution to the system of these linear equations based on the graph.y=−5x+7 y=−2x+10 (1 point)Responses(12,−1) left parenthesis 12 comma negative 1 right parenthesis(−1, 12)left parenthesis negative 1 comma 12 right parenthesis(1,−12) left parenthesis 1 comma negative 12 right parenthesis(−1,−12)

Answer 1

To find the solution to the system of equations given by the lines \( y = -5x + 7 \) and \( y = -2x + 10 \), we can set the two equations equal to each other to find the intersection point, which is the solution to the system.

1. Set the equations equal to each other: \[ -5x + 7 = -2x + 10 \]

2. Rearrange the equation to isolate \( x \): \[ -5x + 2x = 10 - 7 \] \[ -3x = 3 \] \[ x = -1 \]

3. Substitute \( x = -1 \) back into one of the original equations to find \( y \). We can use the first equation: \[ y = -5(-1) + 7 \] \[ y = 5 + 7 \] \[ y = 12 \]

So the solution to the system of equations is \( (-1, 12) \).

Therefore, the estimated solution to the system of linear equations is \((-1, 12)\).