Question

1. solve this system of equations using elimination. show all of your work and write your solution as an ordered pair.

$2x - 7y = -13$
$8x - 7y = 11$

Explanation:

Step1: Subtract the two equations

We have the system:
\[

$$\begin{cases} 2x - 7y = -13 \\ 8x - 7y = 11 \end{cases}$$

\]
Subtract the first equation from the second equation to eliminate \(y\):
\((8x - 7y)-(2x - 7y)=11-(-13)\)
Simplify the left side: \(8x - 7y - 2x + 7y = 6x\)
Simplify the right side: \(11 + 13 = 24\)
So we get \(6x = 24\)

Step2: Solve for \(x\)

Divide both sides of \(6x = 24\) by 6:
\(x=\frac{24}{6}=4\)

Step3: Substitute \(x = 4\) into one of the original equations

Let's use the first equation \(2x - 7y = -13\). Substitute \(x = 4\):
\(2(4)-7y=-13\)
Simplify: \(8 - 7y = -13\)

Step4: Solve for \(y\)

Subtract 8 from both sides: \(-7y=-13 - 8=-21\)
Divide both sides by \(-7\): \(y=\frac{-21}{-7}=3\)

Answer:

The solution as an ordered pair is \((4, 3)\)