Question

solve the system of equations.
-5y + 6x = 40
3y - 8x = -46
x =

y =

Explanation:

Step1: Eliminate y via scaling

Multiply first eq by 3: $3(-5y + 6x) = 3(40) \implies -15y + 18x = 120$
Multiply second eq by 5: $5(3y - 8x) = 5(-46) \implies 15y - 40x = -230$

Step2: Add scaled equations

Add the two new equations:
$(-15y + 18x) + (15y - 40x) = 120 + (-230)$
$\implies -22x = -110$

Step3: Solve for x

Isolate x: $x = \frac{-110}{-22} = 5$

Step4: Substitute x into first equation

Plug $x=5$ into $-5y + 6x = 40$:
$-5y + 6(5) = 40 \implies -5y + 30 = 40$

Step5: Solve for y

Isolate y: $-5y = 40 - 30 = 10 \implies y = \frac{10}{-5} = -2$

Answer:

$x = 5$
$y = -2$