Question

1. \\(-3x - 4y = 2\\)\\(6x + 6y = -6\\)

Explanation:

Step1: Eliminate x variable

Multiply first equation by 2:
$$2(-3x - 4y) = 2(2)$$
$$-6x - 8y = 4$$
Add to second equation:
$$(-6x - 8y) + (6x + 6y) = 4 + (-6)$$
$$-2y = -2$$

Step2: Solve for y

Divide both sides by -2:
$$y = \frac{-2}{-2} = 1$$

Step3: Substitute y into second equation

$$6x + 6(1) = -6$$
$$6x + 6 = -6$$

Step4: Solve for x

Subtract 6 from both sides:
$$6x = -6 - 6 = -12$$
Divide by 6:
$$x = \frac{-12}{6} = -2$$

Answer:

$x=-2$, $y=1$