Question

solve using elimination.
4x + 2y = -12
-2x - 5y = -10
(\boxed{ }, \boxed{ })

Explanation:

Step1: Multiply the second equation by 2 to eliminate x

We have the system of equations:

$$\begin{cases} 4x + 2y = -12 \\ -2x - 5y = -10 \end{cases}$$

Multiply the second equation by 2: $2\times(-2x - 5y)=2\times(-10)$ which gives $-4x - 10y = -20$.

Step2: Add the two equations to eliminate x

Now add the first equation $4x + 2y = -12$ and the new second equation $-4x - 10y = -20$:
$(4x - 4x)+(2y - 10y)=-12 - 20$
Simplify: $-8y=-32$

Step3: Solve for y

Divide both sides of $-8y = -32$ by -8: $y=\frac{-32}{-8}=4$

Step4: Substitute y = 4 into the first equation to solve for x

Substitute y = 4 into $4x + 2y = -12$:
$4x + 2\times4=-12$
$4x + 8=-12$
Subtract 8 from both sides: $4x=-12 - 8=-20$
Divide by 4: $x=\frac{-20}{4}=-5$

Answer:

$(-5, 4)$