Question

$\

$$\begin{cases} 5x - 2y = -16 \\\\ 3x - 7y = 31 \\end{cases}$$

$

Explanation:

Step1: Eliminate x via scaling equations

Multiply first eq by 3: $15x - 6y = -48$
Multiply second eq by 5: $15x - 35y = 155$

Step2: Subtract equations to solve for y

Subtract scaled eq2 from scaled eq1:
$$(15x - 6y) - (15x - 35y) = -48 - 155$$
$$29y = -203$$
$$y = \frac{-203}{29} = -7$$

Step3: Substitute y into first equation

Plug $y=-7$ into $5x - 2y = -16$:
$$5x - 2(-7) = -16$$
$$5x + 14 = -16$$

Step4: Solve for x

$$5x = -16 - 14$$
$$5x = -30$$
$$x = -6$$

Answer:

$x = -6$, $y = -7$