Question

Estimate the solution to the system of these linear equations based on the graph. y=5x+10 y=−2x+3

Answer 1

To estimate the solution to the system of the linear equations \( y = 5x + 10 \) and \( y = -2x + 3 \), we need to find the point where these two lines intersect.

1. **Set the equations equal to each other** since they both equal \( y \):
\[
5x + 10 = -2x + 3
\]

2. **Solve for \( x \)**:
- Add \( 2x \) to both sides:
\[
5x + 2x + 10 = 3
\]
\[
7x + 10 = 3
\]
- Subtract 10 from both sides:
\[
7x = 3 - 10
\]
\[
7x = -7
\]
- Divide by 7:
\[
x = -1
\]

3. **Substitute \( x = -1 \) into one of the original equations to find \( y \)**. We'll use \( y = 5x + 10 \):
\[
y = 5(-1) + 10
\]
\[
y = -5 + 10
\]
\[
y = 5
\]

The solution to the system of equations, which is the point of intersection, is:
\[
\boxed{(-1, 5)}
\]

If you were to graph these equations, you would see that their lines intersect at the point \((-1, 5)\).