Question

1. \

$$\begin{cases}10x + 8y = 0\\\\-5x - 10y = 0\\end{cases}$$

Explanation:

Step1: Simplify first equation

Divide by 2: $5x + 4y = 0$

Step2: Simplify second equation

Divide by -5: $x + 2y = 0$

Step3: Isolate $x$ from Step2

$x = -2y$

Step4: Substitute $x$ into Step1 equation

$5(-2y) + 4y = 0$
$\implies -10y + 4y = 0$
$\implies -6y = 0$

Step5: Solve for $y$

$y = 0$

Step6: Substitute $y$ back to $x=-2y$

$x = -2(0) = 0$

Answer:

$x=0$, $y=0$