Question

$\

$$\begin{cases} -3x - 9y = 18 \\\\ 4x + 3y = 12 \\end{cases}$$

$
$x = \square$
$y = \square$

Explanation:

Step1: Simplify first equation

Divide the first equation by $-3$:
$$\frac{-3x - 9y}{-3} = \frac{18}{-3}$$
$$x + 3y = -6$$

Step2: Label equations for clarity

Let:
Equation (1): $x + 3y = -6$
Equation (2): $4x + 3y = 12$

Step3: Eliminate $y$ via subtraction

Subtract Equation (1) from Equation (2):
$$(4x + 3y) - (x + 3y) = 12 - (-6)$$
$$3x = 18$$

Step4: Solve for $x$

Divide both sides by 3:
$$x = \frac{18}{3} = 6$$

Step5: Substitute $x$ into Equation (1)

$$6 + 3y = -6$$

Step6: Solve for $y$

Subtract 6 from both sides, then divide by 3:
$$3y = -6 - 6 = -12$$
$$y = \frac{-12}{3} = -4$$

Answer:

$x = 6$
$y = -4$