Question

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

Answer 1

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)**.