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

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

GPT-4o mini · Answer

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

$- 5 x + y = - 18$
$10 x - 2 y = 36$

First, we can rearrange both equations to the slope-intercept form $y = m x + b$ , which makes it easier to compare their slopes.

Rearranging the first equation: $y = 5 x - 18$

Rearranging the second equation: $10 x - 2 y = 36$ $- 2 y = - 10 x + 36$ $y = 5 x - 18$

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

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 $y = 5 x - 18$ is a solution.

Therefore, the answer is infinite solutions.