Question

Estimate the solution to the system of these linear equations based on the graph.y=−2x+3y=5x−4(1 point)Responses (-1, 1) (-1, 1) (1, -1) (1, -1) (-1, -1) (-1, -1) (1, 1)

Answer 1

To find the solution to the system of equations given by \( y = -2x + 3 \) and \( y = 5x - 4 \), we can set the equations equal to each other to find the point of intersection:

1. Set the equations equal:
\[
-2x + 3 = 5x - 4
\]

2. Solve for \( x \):
\[
3 + 4 = 5x + 2x
\]
\[
7 = 7x
\]
\[
x = 1
\]

3. Substitute \( x = 1 \) back into either equation to find \( y \). We can use the first equation:
\[
y = -2(1) + 3
\]
\[
y = -2 + 3 = 1
\]

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

Therefore, the correct response is:
- **(1, 1)**