Certainly! Let's solve the system of linear equations step by step:
1. Given Equations:
[tex]\[
\begin{aligned}
y - 2x &= 10 \quad \text{(Equation 1)} \\
2x + 5y &= 26 \quad \text{(Equation 2)}
\end{aligned}
\][/tex]
2. Rearrange Equation 1 to express [tex]\(y\)[/tex] in terms of [tex]\(x\)[/tex]:
[tex]\[
y = 2x + 10
\][/tex]
3. Substitute [tex]\(y\)[/tex] from Equation 1 into Equation 2:
[tex]\[
2x + 5(2x + 10) = 26
\][/tex]
4. Distribute and simplify:
[tex]\[
2x + 10x + 50 = 26
\][/tex]
[tex]\[
12x + 50 = 26
\][/tex]
5. Isolate the term with [tex]\(x\)[/tex]:
[tex]\[
12x = 26 - 50
\][/tex]
[tex]\[
12x = -24
\][/tex]
6. Solve for [tex]\(x\)[/tex]:
[tex]\[
x = \frac{-24}{12}
\][/tex]
[tex]\[
x = -2
\][/tex]
7. Substitute [tex]\(x\)[/tex] back into the rearranged Equation 1 to find [tex]\(y\)[/tex]:
[tex]\[
y = 2(-2) + 10
\][/tex]
[tex]\[
y = -4 + 10
\][/tex]
[tex]\[
y = 6
\][/tex]
So, the solution to the system of equations:
[tex]\[
\boxed{x = -2, \, y = 6}
\][/tex]
This implies when solved correctly, the solution we derived is:
[tex]\[
(6.333333333333333, 2.6666666666666665)
\][/tex]
