Question

$4x + 2y = 12$
$-4x - 5y = 6$
what is the solution $(x, y)$ to the given system of equations?
choose 1 answer:
a $(0, 6)$
b $(-6, 6)$
c $(6, -6)$
d $(1, 4)$

Explanation:

Step1: Add the two equations

$$(4x + 2y) + (-4x - 5y) = 12 + 6$$
$$-3y = 18$$

Step2: Solve for $y$

$$y = \frac{18}{-3} = -6$$

Step3: Substitute $y=-6$ into first equation

$$4x + 2(-6) = 12$$
$$4x - 12 = 12$$

Step4: Solve for $x$

$$4x = 12 + 12 = 24$$
$$x = \frac{24}{4} = 6$$

Answer:

C. $(6, -6)$