Question

do now!
solve the given problem using elimination. show your solutions!
1.) $\begin{cases}-10x + 6y = -8\\\\ -6x + 8y = 26end{cases}$

Explanation:

Step1: Eliminate x, scale equations

Multiply first equation by 3: $3(-10x + 6y) = 3(-8) \implies -30x + 18y = -24$
Multiply second equation by 5: $5(-6x + 8y) = 5(26) \implies -30x + 40y = 130$

Step2: Subtract scaled equations

Subtract first new eq from second:
$(-30x + 40y) - (-30x + 18y) = 130 - (-24)$
$22y = 154$

Step3: Solve for y

$y = \frac{154}{22} = 7$

Step4: Substitute y into original eq

Use $-10x + 6y = -8$:
$-10x + 6(7) = -8$
$-10x + 42 = -8$
$-10x = -8 - 42 = -50$

Step5: Solve for x

$x = \frac{-50}{-10} = 5$

Answer:

$x=5$, $y=7$