To solve the system of equations using the substitution method, follow these steps:
Given system of equations:
[tex]\[
\begin{array}{l}
2 x - y = 10 \quad \text{(Equation 1)} \\
2 x - 2 y = 4 \quad \text{(Equation 2)}
\end{array}
\][/tex]
1. Solve for [tex]\( y \)[/tex] in terms of [tex]\( x \)[/tex] from Equation 1:
[tex]\[
2 x - y = 10
\][/tex]
Rearrange to solve for [tex]\( y \)[/tex]:
[tex]\[
y = 2 x - 10
\][/tex]
2. Substitute the expression for [tex]\( y \)[/tex] into Equation 2:
Substitute [tex]\( y = 2 x - 10 \)[/tex] into [tex]\( 2 x - 2 y = 4 \)[/tex]:
[tex]\[
2 x - 2(2 x - 10) = 4
\][/tex]
3. Simplify and solve for [tex]\( x \)[/tex]:
[tex]\[
2 x - 2(2 x) + 20 = 4 \\
2 x - 4 x + 20 = 4 \\
-2 x + 20 = 4
\][/tex]
Subtract 20 from both sides:
[tex]\[
-2 x = 4 - 20 \\
-2 x = -16
\][/tex]
Divide both sides by -2:
[tex]\[
x = 8
\][/tex]
4. Substitute [tex]\( x = 8 \)[/tex] back into the expression for [tex]\( y \)[/tex]:
Using the expression [tex]\( y = 2 x - 10 \)[/tex]:
[tex]\[
y = 2(8) - 10 \\
y = 16 - 10 \\
y = 6
\][/tex]
5. Conclusion:
The solution to the system of equations is the ordered pair [tex]\((8, 6)\)[/tex].
Therefore, the correct answer is:
[tex]\[
\boxed{(8, 6)}
\][/tex]
