Question

on. clearly identify your solution.

1. $\begin{cases} y=-2x+2 \\ y=7x+11 end{cases}$
2. $\begin{cases} y=2x \\ 5x-y=9 end{cases}$
3. $\begin{cases} x=3y \\ 2x+4y=10 end{cases}$
4. $\begin{cases} 3x-7y=41 \\ x=-2y-21 end{cases}$

Explanation:

Problem 2

Step1: Set equations equal

$-2x + 2 = 7x + 11$

Step2: Solve for $x$

$-2x -7x = 11 - 2$
$-9x = 9$
$x = -1$

Step3: Substitute $x$ to find $y$

$y = -2(-1) + 2 = 2 + 2 = 4$

Problem 4

Step1: Substitute $y=2x$ into equation

$5x - 2x = 9$

Step2: Solve for $x$

$3x = 9$
$x = 3$

Step3: Substitute $x$ to find $y$

$y = 2(3) = 6$

Problem 6

Step1: Substitute $x=3y$ into equation

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

Step2: Solve for $y$

$6y + 4y = 10$
$10y = 10$
$y = 1$

Step3: Substitute $y$ to find $x$

$x = 3(1) = 3$

Problem 8

Step1: Substitute $x=-2y-21$ into equation

$3(-2y - 21) - 7y = 41$

Step2: Solve for $y$

$-6y - 63 -7y = 41$
$-13y = 41 + 63$
$-13y = 104$
$y = -8$

Step3: Substitute $y$ to find $x$

$x = -2(-8) -21 = 16 -21 = -5$

Answer:

1. $x=-1$, $y=4$
2. $x=3$, $y=6$
3. $x=3$, $y=1$
4. $x=-5$, $y=-8$