Question

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

(−1,−5) left parenthesis negative 1 comma negative 5 right parenthesis (−1, 5) left parenthesis negative 1 comma 5 right parenthesis (5,−1) left parenthesis 5 comma negative 1 right parenthesis (1, 5)

Answer 1

To find the intersection point of the two equations \( y = 5x + 10 \) and \( y = -2x + 3 \), we can set them equal to each other:

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

Next, we can 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 by \( 7 \):
\[
x = -1
\]

Now that we have \( x = -1 \), we can substitute this value back into either equation to find \( y \). Let's use the second equation:

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

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

Based on the options you've provided, the correct answer is:
**(−1, 5)**.