Question

2x - 3y = 24\
3x + 2y = -3

Explanation:

Step1: Eliminate y, scale equations

Multiply first eq by 2: $4x - 6y = 48$
Multiply second eq by 3: $9x + 6y = -9$

Step2: Add scaled equations

$$(4x - 6y) + (9x + 6y) = 48 + (-9)$$
$$13x = 39$$

Step3: Solve for x

$$x = \frac{39}{13} = 3$$

Step4: Substitute x=3 into second eq

$$3(3) + 2y = -3$$
$$9 + 2y = -3$$

Step5: Solve for y

$$2y = -3 - 9 = -12$$
$$y = \frac{-12}{2} = -6$$

Answer:

$x=3$, $y=-6$