To estimate the solution to the system of linear equations given by \( y = -5x + 7 \) and \( y = -2x + 10 \), we can find the point of intersection of these two lines.
First, we can set the two equations equal to each other to find the x-coordinate of the intersection:
\[ -5x + 7 = -2x + 10 \]
Now, rearranging the equation:
\[ -5x + 2x = 10 - 7 \] \[ -3x = 3 \] \[ x = -1 \]
Next, we substitute \( x = -1 \) back into one of the original equations to find the y-coordinate. Let's use \( y = -5x + 7 \):
\[ y = -5(-1) + 7 \] \[ y = 5 + 7 \] \[ y = 12 \]
Thus, the intersection point of the two lines, which is the solution to the system of equations, is \( (-1, 12) \).
Looking at the response options you provided, the correct solution is:
(−1, 12).