How many solution(s) does the system of equations have?

Question

−5x+y=−18

10x−2y=36
(1 point)
Responses

infinite
infinite

none
none

one
one

two

Answer 1

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

1. The first equation is: \(-5x + y = -18\)

2. The second equation is: \(10x - 2y = 36\)

We can rearrange the first equation to express \(y\) in terms of \(x\): \[ y = 5x - 18 \]

Now, we can also rearrange the second equation to isolate \(y\): \[ 10x - 2y = 36 \implies -2y = -10x + 36 \implies y = 5x - 18 \]

Notice that both equations simplify to the same equation \(y = 5x - 18\). This indicates that both equations represent the same line.

Since both equations represent the same line, they intersect at an infinite number of points. Therefore, the system of equations has:

infinite solutions.