Question

−5x+y=−18

10x−2y=36
(1 point)
Responses

two
two

infinite
infinite

one
one

none

Answer 1

To determine how many solutions the system of equations has, we need to analyze the two equations:

1. \(-5x + y = -18\)
2. \(10x - 2y = 36\)

Let's solve the first equation for \(y\) to find its slope and y-intercept:

\[
y = 5x - 18
\]

Next, we'll rearrange the second equation. We can simplify it by dividing everything by 2:

\[
5x - y = 18 \quad \text{(after rearranging this we find: } y = 5x - 18\text{)}
\]

Now we can see that both equations represent the line \(y = 5x - 18\).

Since both equations describe the same line, they have infinitely many solutions (any point on the line is a solution).

Hence, the correct response is:

**infinite**