Question

solve using elimination. 8x + 8y = 8 -10x - 8y = 10

Explanation:

Step1: Add the two equations

Add the equations \(8x + 8y = 8\) and \(-10x - 8y = 10\) together. The \(8y\) and \(-8y\) will eliminate each other.
\[

$$\begin{align*} (8x + 8y) + (-10x - 8y) &= 8 + 10\\ 8x + 8y - 10x - 8y &= 18\\ -2x &= 18 \end{align*}$$

\]

Step2: Solve for x

Divide both sides of the equation \(-2x = 18\) by \(-2\) to find the value of \(x\).
\[
x=\frac{18}{-2}=-9
\]

Step3: Substitute x into one of the original equations

Substitute \(x = -9\) into the first equation \(8x + 8y = 8\).
\[
8(-9)+8y = 8
\]
\[
-72 + 8y = 8
\]

Step4: Solve for y

Add 72 to both sides of the equation \(-72 + 8y = 8\).
\[
8y=8 + 72
\]
\[
8y = 80
\]
Divide both sides by 8.
\[
y=\frac{80}{8}=10
\]

Answer:

\((-9, 10)\)