Question

How many solution(s) does the system of equations have?
−5x+y=−18
10x−2y=36 (1 point)
Responses

two
two

one
one

infinite
infinite

none

Answer 1

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

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

First, we can rearrange both equations to the slope-intercept form \(y = mx + b\), which makes it easier to compare their slopes.

**Rearranging the first equation:**
\[
y = 5x - 18
\]

**Rearranging the second equation:**
\[
10x - 2y = 36
\]
\[
-2y = -10x + 36
\]
\[
y = 5x - 18
\]

Now we have both equations in the form of \(y = 5x - 18\).

Since both equations are identical, they represent the same line. This means that there are infinitely many solutions to this system of equations, as any point on the line \(y = 5x - 18\) is a solution.

Therefore, the answer is **infinite solutions**.