Question

solve each system using the method of your choice. homework help
a. $8y - x = 1$
$10y = x + 5$
b. $5y = 2 - 6x$
$y - 2x = 10$

Explanation:

Part a:

Step1: Rearrange first equation

$x = 8y - 1$

Step2: Substitute into second equation

$10y = (8y - 1) + 5$

Step3: Simplify to solve for y

$10y = 8y + 4$
$10y - 8y = 4$
$2y = 4$
$y = 2$

Step4: Substitute y back to find x

$x = 8(2) - 1 = 16 - 1 = 15$

Part b:

Step1: Rearrange second equation

$y = 2x + 10$

Step2: Substitute into first equation

$5(2x + 10) = 2 - 6x$

Step3: Simplify to solve for x

$10x + 50 = 2 - 6x$
$10x + 6x = 2 - 50$
$16x = -48$
$x = -3$

Step4: Substitute x back to find y

$y = 2(-3) + 10 = -6 + 10 = 4$

Answer:

a. $x=15$, $y=2$
b. $x=-3$, $y=4$