Question

1. \

$$\begin{cases}6x + 4y = -28 \\\\ 3x + 8y = -20\\end{cases}$$

Explanation:

Step1: Eliminate x variable

Multiply the second equation by -2:
$$-2\times(3x + 8y) = -2\times(-20)$$
$$-6x - 16y = 40$$

Step2: Add to first equation

Add the new equation to the first original equation to eliminate $x$:
$$(6x + 4y) + (-6x - 16y) = -28 + 40$$
$$-12y = 12$$

Step3: Solve for y

Divide both sides by -12:
$$y = \frac{12}{-12} = -1$$

Step4: Substitute y into second equation

Plug $y=-1$ into $3x + 8y = -20$:
$$3x + 8\times(-1) = -20$$
$$3x - 8 = -20$$

Step5: Solve for x

Add 8 to both sides, then divide by 3:
$$3x = -20 + 8 = -12$$
$$x = \frac{-12}{3} = -4$$

Answer:

$x=-4$, $y=-1$