Sure, let's solve the system of equations step by step using the linear combination method:
Given the system:
[tex]\[
\begin{cases}
-3x + 8y = 16 \\
3x + 4y = 8
\end{cases}
\][/tex]
1. Add the two equations to eliminate [tex]\(x\)[/tex]:
[tex]\[
(-3x + 8y) + (3x + 4y) = 16 + 8
\][/tex]
2. Combine like terms:
[tex]\[
-3x + 3x + 8y + 4y = 24
\][/tex]
[tex]\[
12y = 24
\][/tex]
3. Solve for [tex]\(y\)[/tex]:
[tex]\[
y = \frac{24}{12} = 2
\][/tex]
4. Substitute [tex]\(y = 2\)[/tex] back into one of the original equations to solve for [tex]\(x\)[/tex]. Using the second equation [tex]\(3x + 4y = 8\)[/tex]:
[tex]\[
3x + 4(2) = 8
\][/tex]
[tex]\[
3x + 8 = 8
\][/tex]
5. Isolate [tex]\(x\)[/tex]:
[tex]\[
3x = 8 - 8
\][/tex]
[tex]\[
3x = 0
\][/tex]
[tex]\[
x = \frac{0}{3} = 0
\][/tex]
Hence, the value of [tex]\(x\)[/tex] is [tex]\(\boxed{0}\)[/tex].
