Question

3x + 2y = -26\
4x - 5y = -4

Explanation:

Step1: Eliminate x via scaling equations

Multiply first eq by 4: $12x + 8y = -104$
Multiply second eq by 3: $12x - 15y = -12$

Step2: Subtract equations to solve y

Subtract scaled second eq from first:
$$(12x + 8y) - (12x - 15y) = -104 - (-12)$$
$$23y = -92$$
$$y = \frac{-92}{23} = -4$$

Step3: Substitute y into second equation

$$4x - 5(-4) = -4$$
$$4x + 20 = -4$$

Step4: Solve for x

$$4x = -4 - 20 = -24$$
$$x = \frac{-24}{4} = -6$$

Answer:

$x = -6$, $y = -4$