Question

-3x - 8y = 20
-5x + y = 19

-3x + 3y = 3
-5x + y = 13

Explanation:

First System of Equations: $-3x - 8y = 20$ and $-5x + y = 19$

Step1: Solve for $y$ from the second equation

$y = 5x + 19$

Step2: Substitute $y$ into the first equation

$-3x - 8(5x + 19) = 20$
$-3x - 40x - 152 = 20$
$-43x = 172$
$x = -4$

Step3: Substitute $x=-4$ into $y=5x+19$

$y = 5(-4) + 19 = -20 + 19 = -1$

Second System of Equations: $-3x + 3y = 3$ and $-5x + y = 13$

Step1: Simplify the first equation

Divide by 3: $-x + y = 1$ → $y = x + 1$

Step2: Substitute $y$ into the second equation

$-5x + (x + 1) = 13$
$-4x + 1 = 13$
$-4x = 12$
$x = -3$

Step3: Substitute $x=-3$ into $y=x+1$

$y = -3 + 1 = -2$

Answer:

$x = -4$, $y = -1$