Question

Estimate the solution to the system of these linear equations based on the graph.
y = 5x + 10
y = -2x + 3
(1 point)
О (5, -1)
O (-1,-5)
O (-1,5)
O (1,5)

Answer 1

To estimate the solution to the system of equations based on the graph, we need to find the point of intersection between the two given lines:

1. **Equation 1**: \( y = 5x + 10 \)
2. **Equation 2**: \( y = -2x + 3 \)

To find the intersection point, we can set the two equations equal to each other:

\[
5x + 10 = -2x + 3
\]

Now, let's solve for \( x \):

1. Add \( 2x \) to both sides:

\[
5x + 2x + 10 = 3
\]
\[
7x + 10 = 3
\]

2. Subtract \( 10 \) from both sides:

\[
7x = 3 - 10
\]
\[
7x = -7
\]

3. Divide both sides by \( 7 \):

\[
x = -1
\]

Now, substitute \( x = -1 \) back into either of the original equations to find \( y \). We can use the second equation:

\[
y = -2(-1) + 3
\]
\[
y = 2 + 3 = 5
\]

Thus, the point of intersection, which is the solution to the system, is:

\[
(-1, 5)
\]

Now, we can select the correct answer choice based on the options provided:

- O (5, -1)
- O (-1, -5)
- O (-1, 5) **(This is our correct answer)**
- O (1, 5)

The correct choice is **O (-1, 5)**.