To solve the system of equations:
[tex]\[
\begin{cases}
x + 2y = 22 \\
x - y = -2
\end{cases}
\][/tex]
we can use the method of elimination or substitution. Here’s a step-by-step solution using the elimination method:
1. Write down the system of equations:
[tex]\[
\begin{cases}
x + 2y = 22 \\
x - y = -2
\end{cases}
\][/tex]
2. Eliminate one of the variables (let's eliminate [tex]\(x\)[/tex]):
- We have the first equation: [tex]\(x + 2y = 22\)[/tex].
- We have the second equation: [tex]\(x - y = -2\)[/tex].
3. Subtract the second equation from the first equation:
[tex]\[
(x + 2y) - (x - y) = 22 - (-2)
\][/tex]
4. Simplify the equation:
[tex]\[
x + 2y - x + y = 22 + 2
\][/tex]
[tex]\[
3y = 24
\][/tex]
5. Solve for [tex]\(y\)[/tex]:
[tex]\[
y = \frac{24}{3} = 8
\][/tex]
6. Substitute the value of [tex]\(y\)[/tex] back into one of the original equations to find [tex]\(x\)[/tex]:
- Using the second equation: [tex]\(x - y = -2\)[/tex]:
[tex]\[
x - 8 = -2
\][/tex]
[tex]\[
x = -2 + 8
\][/tex]
[tex]\[
x = 6
\][/tex]
Therefore, the solution to the system of equations is [tex]\(x = 6\)[/tex] and [tex]\(y = 8\)[/tex].
So, the correct answer is:
[tex]\[ 6.0, 8.0 \][/tex]
