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

Question

−5x+y=−18

10x−2y=36
(1 point)
Responses

none
none

two
two

one
one

infinite

Answer 1

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

1. First equation:
   \(-5x + y = -18\)

2. Second equation:
   \(10x - 2y = 36\)

Let's simplify the second equation. Divide the entire equation by 2:

\[ 5x - y = 18 \]

Now we will rewrite the first equation in terms of \(y\):

From \(-5x + y = -18\), we can express \(y\) as:

\[ y = 5x - 18 \]

Now, we have two equations in terms of \(y\):

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

Since both equations represent the same line (the first equation rearranged results in the second), it follows that every point on that line is a solution to the system.

Thus, the system has infinite solutions.

The correct response is: infinite.