Question

1. \

$$\begin{cases}4x + y = 1 \\\\ x - 2y = 16\\end{cases}$$

Explanation:

Step1: Isolate y from first equation

From $4x + y = 1$, rearrange to get:
$y = 1 - 4x$

Step2: Substitute y into second equation

Replace y in $x - 2y = 16$:
$x - 2(1 - 4x) = 16$
Expand and simplify:
$x - 2 + 8x = 16$
$9x - 2 = 16$

Step3: Solve for x

Add 2 to both sides, then divide by 9:
$9x = 16 + 2 = 18$
$x = \frac{18}{9} = 2$

Step4: Substitute x to find y

Use $y = 1 - 4x$ with $x=2$:
$y = 1 - 4(2) = 1 - 8 = -7$

Answer:

$x=2$, $y=-7$