Question

solve the following system using the substitution method.
$3x - 2y = -16$
$5x + 10y = 0$

Explanation:

Step1: Simplify second equation

Divide $5x + 10y = 0$ by 5:
$x + 2y = 0$
Rearrange to solve for $x$:
$x = -2y$

Step2: Substitute $x=-2y$ into first equation

Substitute $x=-2y$ into $3x - 2y = -16$:
$3(-2y) - 2y = -16$

Step3: Solve for $y$

Calculate and combine like terms:
$-6y - 2y = -16$
$-8y = -16$
Divide both sides by $-8$:
$y = \frac{-16}{-8} = 2$

Step4: Solve for $x$

Substitute $y=2$ into $x=-2y$:
$x = -2(2) = -4$

Answer:

$x=-4$, $y=2$