Question

Estimate the solution to the system of these linear equations based on the graph.

y=5x+10
𝑦
=
5
𝑥
+
10

y=−2x+3
𝑦
=
−
2
𝑥
+
3

(1 point)
Responses

(1, 5)
(
1
,

Answer 1

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

Here is a quick way to solve for the intersection algebraically:

1. Set the equations equal to each other:
\[
5x + 10 = -2x + 3
\]

2. Combine like terms:
\[
5x + 2x = 3 - 10
\]
\[
7x = -7
\]

3. Solve for \( x \):
\[
x = -1
\]

4. Substitute \( x = -1 \) into either equation to find \( y \). We'll use \( y = 5x + 10 \):
\[
y = 5(-1) + 10 = -5 + 10 = 5
\]

Thus, the point of intersection is \( (-1, 5) \).

So, the estimated solution to the system of equations is:
\[
\boxed{(-1, 5)}
\]