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

Question

infinite infinite

one one

none none

two

Answer 1

To determine how many solutions the system of equations has, we can start by rearranging and analyzing the given equations:

1. The first equation is: \[ -5x + y = -18 \implies y = 5x - 18 \]

2. The second equation is: \[ 10x - 2y = 36 \implies -2y = -10x + 36 \implies y = 5x - 18 \]

Now, we can see that both equations simplify to the same equation: \[ y = 5x - 18 \]

Since both equations describe the same line, they have infinitely many solutions (any point on the line satisfies both equations).

Thus, the answer is: infinite infinite