Question

1. $(-x + 11y = -9)(10)$

$-10x - y = 21$

1. $12x + 9y = 0$

$(3x + 5y = 11)(-4)$

1. $-4x + 10y = -4$

$(-10x + y = -10)(-10)$

1. $8x + 8y = 8$

$-7x - 16y = 2$

1. $4x + 10y = -20$

$-3x - 5y = 5$

1. $4x - 9y = 17$

$2x + 18y = -14$

1. $14x + y = 9$

$7x - 3y = 22$

1. $-4x - 9y = 5$

$-10x - 18y = -10$

Explanation:

Let's solve problem 9 as an example (system of linear equations using elimination):

Step 1: Multiply the first equation by 10 to eliminate x

The system is:

$$\begin{cases} -x + 11y = -9 \\ -10x - y = 21 \end{cases}$$

Multiply the first equation by 10:
$10(-x + 11y) = 10(-9)$
$\Rightarrow -10x + 110y = -90$

Step 2: Subtract the second equation from the new first equation

New first equation: $-10x + 110y = -90$
Second equation: $-10x - y = 21$

Subtract (second equation) from (new first equation):
$(-10x + 110y) - (-10x - y) = -90 - 21$
$\Rightarrow -10x + 110y + 10x + y = -111$
$\Rightarrow 111y = -111$

Step 3: Solve for y

Divide both sides by 111:
$y = \frac{-111}{111} = -1$

Step 4: Substitute y = -1 into the first original equation to find x

First original equation: $-x + 11y = -9$
Substitute $y = -1$:
$-x + 11(-1) = -9$
$\Rightarrow -x - 11 = -9$
Add 11 to both sides:
$-x = 2$
Multiply both sides by -1:
$x = -2$

Answer:

The solution is $x = -2$, $y = -1$ (or the ordered pair $(-2, -1)$).