Question

solve using elimination.
-5x + 3y = 13
-x - y = 9
(\boxed{\quad}, \boxed{\quad})

Explanation:

Step1: Multiply the second equation to eliminate y

We have the system:

$$\begin{cases} -5x + 3y = 13 \\ -x - y = 9 \end{cases}$$

Multiply the second equation by 3: $3(-x - y)=3\times9$ which gives $-3x - 3y = 27$.

Step2: Add the two equations

Now add the first equation $-5x + 3y = 13$ and the new second equation $-3x - 3y = 27$:
$$(-5x + 3y)+(-3x - 3y)=13 + 27$$
Simplify: $-8x=40$.

Step3: Solve for x

Divide both sides by -8: $x=\frac{40}{-8}=-5$.

Step4: Substitute x into an equation to find y

Substitute $x = -5$ into the second original equation $-x - y = 9$:
$-(-5)-y = 9$ which simplifies to $5 - y = 9$.
Subtract 5 from both sides: $-y = 9 - 5 = 4$.
Multiply both sides by -1: $y=-4$.

Answer:

$(-5, -4)$