Question

kuta software - infinite algebra 1
solving systems of equations by eliminati
solve each system by elimination.

1. $-4x - 2y = -12$

$4x + 8y = -24$

Explanation:

Step1: Add the two equations

We have the system:
$$-4x - 2y = -12$$
$$4x + 8y = -24$$
Adding them together: $(-4x - 2y)+(4x + 8y)=-12+(-24)$
Simplify: $(-4x + 4x)+(-2y + 8y)=-36$ → $6y=-36$

Step2: Solve for y

Divide both sides by 6: $\frac{6y}{6}=\frac{-36}{6}$ → $y = - 6$

Step3: Substitute y into one equation

Substitute $y=-6$ into $4x + 8y=-24$:
$4x+8(-6)=-24$ → $4x-48=-24$

Step4: Solve for x

Add 48 to both sides: $4x-48 + 48=-24 + 48$ → $4x=24$
Divide by 4: $\frac{4x}{4}=\frac{24}{4}$ → $x = 6$

Answer:

The solution to the system is $x = 6$, $y=-6$