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 examine the equations:

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

First, let's rearrange the first equation to express \(y\) in terms of \(x\):

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

Next, simplify the second equation:
\[
10x - 2y = 36
\]

We can also rearrange this second equation to express \(y\) in terms of \(x\). Start by isolating \(2y\):
\[
2y = 10x - 36
\]
Now divide everything by 2:
\[
y = 5x - 18
\]

Now we have:
1. \(y = 5x - 18\)
2. \(y = 5x - 18\)

Both equations are identical. Since they represent the same line, every point on that line is a solution to the system of equations.

Thus, the system of equations has **infinite solutions**.

The correct response is **infinite**.