Question

solve using elimination.
4x + 8y = 20
-4x + 2y = -30
options: (-7,1), (-2,5), (7,-1), (2,-5)

Explanation:

Step1: Add the two equations to eliminate \(x\)

We have the system of equations:
\[

$$\begin{cases} 4x + 8y = 20 \\ -4x + 2y = -30 \end{cases}$$

\]
Adding the left - hand sides and the right - hand sides of the two equations respectively:
\((4x + 8y)+(-4x + 2y)=20+(-30)\)
Simplify the left - hand side: \(4x-4x + 8y+2y=10y\)
Simplify the right - hand side: \(20 - 30=-10\)
So we get the equation \(10y=-10\)

Step2: Solve for \(y\)

From \(10y=-10\), divide both sides of the equation by 10:
\(y=\frac{-10}{10}=-1\)

Step3: Substitute \(y = - 1\) into one of the original equations to solve for \(x\)

Let's substitute \(y=-1\) into the first equation \(4x + 8y = 20\)
We have \(4x+8\times(-1)=20\)
Simplify: \(4x-8 = 20\)
Add 8 to both sides of the equation: \(4x=20 + 8=28\)
Divide both sides by 4: \(x=\frac{28}{4}=7\)

Answer:

\((7,-1)\)