Question

practice b: solve each system using elimination.

1. \

$$\begin{cases} -6x - 4y = -22 \\\\ -4x - 9y = -2 \\end{cases}$$

Explanation:

Step1: Eliminate $x$ terms.

Multiply first equation by 2: $2(-6x - 4y) = 2(-22) \implies -12x - 8y = -44$
Multiply second equation by 3: $3(-4x - 9y) = 3(-2) \implies -12x - 27y = -6$

Step2: Subtract equations to eliminate $x$.

$(-12x - 8y) - (-12x - 27y) = -44 - (-6)$
$\implies -12x -8y +12x +27y = -38$
$\implies 19y = -38$

Step3: Solve for $y$.

$y = \frac{-38}{19} = -2$

Step4: Substitute $y=-2$ into first equation.

$-6x -4(-2) = -22$
$\implies -6x +8 = -22$

Step5: Solve for $x$.

$-6x = -22 -8 = -30$
$\implies x = \frac{-30}{-6} = 5$

Answer:

$x=5$, $y=-2$