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Solve using elimination. $\newline$ $-9x - 9y = -9$ $\newline$ $-7x - 9y = 9$ $\newline$ (_, _)

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Solve a system of equations using elimination

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Q. Solve using elimination.

\newline

-9x - 9y = -9

\newline

-7x - 9y = 9

\newline

(_____, _____)

Set Up Equations: First, we need to set up the equations in a way that will allow us to eliminate one of the variables when we add or subtract the equations from each other. $\newline$ The given system of equations is: $\newline$ $-9x - 9y = -9$ $\newline$ $-7x - 9y = 9$
Eliminate Variables: To use elimination, we look for a way to cancel out one of the variables. In this case, we can add the two equations together to eliminate the $y$ variable because the coefficients of $y$ are the same (but opposite in sign). $\newline$ We add the equations: $\newline$ $(-9x - 9y) + (-7x + 9y) = -9 + 9$
Perform Addition: Now we perform the addition: $\newline$ $-9x + (-7x) = -16x$ $\newline$ $-9y + 9y = 0$ (y terms cancel out) $\newline$ $-9 + 9 = 0$ $\newline$ So we are left with: $\newline$ $-16x = 0$
Solve for x: Next, we solve for $x$ by dividing both sides of the equation by $–16$ : $\frac{–16x}{–16} = \frac{0}{–16}$ $x = 0$
Substitute $x$ : Now that we have the value of $x$ , we can substitute it back into one of the original equations to find the value of $y$ . We'll use the first equation: $\newline$ $–9x − 9y = –9$ $\newline$ Substitute $x = 0$ : $\newline$ $–9(0) − 9y = –9$ $\newline$ $0 − 9y = –9$
Solve for y: Now we solve for y by dividing both sides of the equation by $–9$ : $\frac{–9y}{–9} = \frac{–9}{–9}$ $y = 1$
Final Solution: We have found the values of $x$ and $y$ . The solution to the system of equations is: $x = 0$ , $y = 1$

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