Question

1. solve the system by elimination.

$8x + 4y = 20$
$2(-4x - y = -15)$
$8x + 4y = 20$
$-8x - 2y = -30$
$\frac{2y = -10}{2} = -5y$
$8x + 4(-5) = 20$
$8x - 20 = 20$
$\frac{8x + 20 = 20 + 20}{8x = 40 = 5}$
$(5, -5)$
(do not sol

Explanation:

Step1: Eliminate $x$ variable

Multiply the second equation by 2:
$$2(-4x - y) = 2(-15) \implies -8x - 2y = -30$$
Add to the first equation:
$$8x + 4y + (-8x - 2y) = 20 + (-30)$$

Step2: Solve for $y$

Simplify and isolate $y$:
$$2y = -10$$
$$y = \frac{-10}{2} = -5$$

Step3: Substitute $y=-5$ to find $x$

Plug $y=-5$ into $8x + 4y = 20$:
$$8x + 4(-5) = 20$$
$$8x - 20 = 20$$

Step4: Solve for $x$

Isolate $x$:
$$8x = 20 + 20 = 40$$
$$x = \frac{40}{8} = 5$$

Answer:

The solution to the system is $(5, -5)$