Question

Question was provided via image upload.

Explanation:

Step1: Eliminate one variable

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

Step2: Add to second equation

Add the new equation to $-9x -5y = -24$:
$$(5x + 5y) + (-9x -5y) = 0 + (-24)$$
$$5x -9x +5y -5y = -24$$
$$-4x = -24$$

Step3: Solve for $x$

Divide both sides by $-4$:
$$x = \frac{-24}{-4} = 6$$

Step4: Solve for $y$

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

Answer:

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