Determine if the following system of equations has no solutions, infinitely many solutions or exactly one solution. {:[x+y=-9],[-x-y=9]:} 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.  {:[x+y=-9],[-x-y=9]:} No Solutions Infinitely Many Solutions One Solution

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Write Equations: Write down the system of equations. We have the system: {:[x+y=-9],[-x-y=9]:}Add Equations: Add the two equations together to see if they are consistent or inconsistent. Adding the equations, we get: (x + y) + (-x - y) = -9 + 9 This simplifies to: 0 = 0Interpret Result: Interpret the result of the addition. Since 0 = 0 is a true statement, it means that the two equations are dependent, and the system has infinitely many solutions.Confirm Equations: Confirm that the equations are indeed the same. Multiplying the second equation by -1, we get: x + y = -9 This is the same as the first equation, confirming that the system has infinitely many solutions.

Determine if the following system of equations has no solutions, infinitely many solutions or exactly one solution. $\newline$ $\begin{aligned} x+y & =-9 \\ -x-y & =9 \end{aligned}$ $\newline$ No Solutions $\newline$ Infinitely Many Solutions $\newline$ One Solution

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