Determine if the following system of equations has no solutions, infinitely many solutions or exactly one solution. {:[-2x+y=-5],[2x-y=5]:} No Solutions Infinitely Many Solutions One Solution

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Determine if the following system of equations has no solutions, infinitely many solutions or exactly one solution.  {:[-2x+y=-5],[2x-y=5]:} No Solutions Infinitely Many Solutions One Solution

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Analyze Equations: Analyze the system of equations. We have the system: -2x + y = -5 2x - y = 5 We will first check if the equations are multiples of each other, which would indicate that they are the same line and therefore have infinitely many solutions.Eliminate y: Add the two equations together to eliminate y. (-2x + y) + (2x - y) = -5 + 5 This simplifies to: 0 = 0 Since the variables cancel out and we are left with a true statement, this indicates that the two equations are indeed the same line.Conclude Solutions: Conclude the number of solutions. Because the two equations represent the same line, the system has infinitely many solutions.

Determine if the following system of equations has no solutions, infinitely many solutions or exactly one solution. $\newline$ $\begin{aligned} -2 x+y & =-5 \\ 2 x-y & =5 \end{aligned}$ $\newline$ No Solutions $\newline$ Infinitely Many Solutions $\newline$ One Solution

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