Question

Question How many solution(s) does the system of equations have? −5x+y=−18 10x−2y=36 (1 point) Responses two two none none infinite infinite one

Answer 1

To determine the number of solutions for the given system of equations, we can first rearrange the equations and then analyze their slopes and intercepts.

The system is:
1. \(-5x + y = -18\)
2. \(10x - 2y = 36\)

Let's rewrite them in slope-intercept form \(y = mx + b\).

1. From \(-5x + y = -18\):
\[
y = 5x - 18
\]

2. From \(10x - 2y = 36\), we can rearrange it:
\[
-2y = -10x + 36 \implies y = 5x - 18
\]

Now, we see that both equations simplify to the same line: \(y = 5x - 18\).

Since both equations represent the same line, they intersect at infinitely many points. Therefore, the system of equations has **infinite solutions**.

So the answer is: **infinite**.