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Question How many solution(s) does the system of equations have? −5x+y=−18 10x−2y=36(1 point) Responses infinite infinite one one none none two

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

  1. The first equation is: \[ -5x + y = -18 \] This can be rewritten as: \[ y = 5x - 18 \]

  2. The second equation is: \[ 10x - 2y = 36 \] We can simplify this by dividing the entire equation by 2: \[ 5x - y = 18 \] This can be rewritten as: \[ y = 5x - 18 \]

Now we observe that both equations can be expressed as: \[ y = 5x - 18 \]

Since both equations represent the same line, they intersect at every point on that line. Therefore, the system has infinitely many solutions.

The correct response is: infinite.