Question

Estimate the solution to the system of these linear equations based on the graph. y=5x+10 y=−2x+3 (1 point) Responses (5,−1) left parenthesis 5 comma negative 1 right parenthesis (1, 5) left parenthesis 1 comma 5 right parenthesis (−1,−5) left parenthesis negative 1 comma negative 5 right parenthesis (−1, 5)

Answer 1

To estimate the solution to the system of linear equations given by the equations \( y = 5x + 10 \) and \( y = -2x + 3 \), we can find the intersection point by setting the two equations equal to each other:

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

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

1. Add \( 2x \) to both sides:
\[
5x + 2x + 10 = 3
\]
This simplifies to:
\[
7x + 10 = 3
\]

2. Subtract \( 10 \) from both sides:
\[
7x = 3 - 10
\]
This simplifies to:
\[
7x = -7
\]

3. Divide both sides by \( 7 \):
\[
x = -1
\]

Now, substitute \( x = -1 \) back into one of the original equations to find \( y \). We'll use \( y = -2x + 3 \):

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

Thus, the solution to the system of equations (the point of intersection) is \( (-1, 5) \).

Based on the given choices:

- (5, -1)
- (1, 5)
- (-1, -5)
- (-1, 5)

The correct response is \((-1, 5)\).