Question

solve the system of equations $x + y = 0$ and $-9x - 5y = -24$ by combining the equations.
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$$\begin{cases} (x + y = 0)\\ (-9x - 5y = -24) \\end{cases}$$

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$$\begin{align*} x + y &= 0\\ -9x - 5y &= -24\\ \\hline x + y&= \\end{align*}$$

Explanation:

Step1: Eliminate y via scaling first eq

Multiply first equation by 5:
$$5(x + y) = 5(0) \implies 5x + 5y = 0$$

Step2: Add to second equation

Add scaled eq to second eq to cancel y:

$$\begin{align} 5x + 5y &= 0 \\ -9x - 5y &= -24 \\ \hline -4x + 0y &= -24 \end{align}$$

Step3: Solve for x

Isolate x by dividing by -4:
$$x = \frac{-24}{-4} = 6$$

Step4: Substitute x to find y

Plug $x=6$ into $x+y=0$:
$$6 + y = 0 \implies y = -6$$

Answer:

$x=6$, $y=-6$