Question

3x - 10y = -84\
x + 5y = 47

Explanation:

Step1: Scale second equation to eliminate $y$

Multiply $x + 5y = 47$ by 2:
$2(x + 5y) = 2\times47$
$2x + 10y = 94$

Step2: Add equations to eliminate $y$

Add $3x - 10y = -84$ and $2x + 10y = 94$:
$(3x - 10y) + (2x + 10y) = -84 + 94$
$5x = 10$

Step3: Solve for $x$

Divide both sides by 5:
$x = \frac{10}{5} = 2$

Step4: Substitute $x$ to find $y$

Plug $x=2$ into $x + 5y = 47$:
$2 + 5y = 47$
$5y = 47 - 2 = 45$
$y = \frac{45}{5} = 9$

Answer:

$x=2$, $y=9$