Question

Use the image to answer the question.
y = -5x + 7
y = -2x + 10
Estimate the solution to the system of these linear equations based on the graph.
y = -5x + 7
y = -2x + 10
A. (-1, -12)
B. (1, -12)
C. (12, -1)
D. (-1, 12

Answer 1

To determine the solution to the system of linear equations based on the equations provided:

1. **Equation 1:** \( y = -5x + 7 \)
2. **Equation 2:** \( y = -2x + 10 \)

To find the intersection point of these lines, we can either graph both equations and look for the point where they intersect or solve the equations algebraically. However, since we are asked to estimate based on a graph and no graph is provided, we can solve the equations algebraically.

Set the two equations equal to each other:

\[
-5x + 7 = -2x + 10
\]

Now, solve for \( x \):

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

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

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

Now substitute \( x = -1 \) back into one of the original equations to find \( y \). Let's use the second equation:

\[
y = -2(-1) + 10 = 2 + 10 = 12
\]

So the point is \( (-1, 12) \).

Therefore, based on our calculations, the estimated solution to the system of linear equations is:

**D. (-1, 12)**