Let's solve this system of linear equations step by step:
1. Write down the given system of equations:
[tex]\[
\begin{cases}
2x + y = 18 \\
y = 2x - 10
\end{cases}
\][/tex]
2. Use the second equation to express [tex]\( y \)[/tex] in terms of [tex]\( x \)[/tex]:
[tex]\[
y = 2x - 10
\][/tex]
3. Substitute [tex]\( y = 2x - 10 \)[/tex] into the first equation [tex]\( 2x + y = 18 \)[/tex]:
[tex]\[
2x + (2x - 10) = 18
\][/tex]
4. Simplify the equation:
[tex]\[
2x + 2x - 10 = 18
\][/tex]
Combine like terms:
[tex]\[
4x - 10 = 18
\][/tex]
5. Solve for [tex]\( x \)[/tex]:
[tex]\[
4x - 10 = 18
\][/tex]
Add 10 to both sides:
[tex]\[
4x = 28
\][/tex]
Divide by 4:
[tex]\[
x = 7
\][/tex]
6. Now that we have [tex]\( x \)[/tex], we substitute [tex]\( x = 7 \)[/tex] back into the second equation to find [tex]\( y \)[/tex]:
[tex]\[
y = 2x - 10
\][/tex]
Substitute [tex]\( x = 7 \)[/tex]:
[tex]\[
y = 2(7) - 10
\][/tex]
Simplify:
[tex]\[
y = 14 - 10 = 4
\][/tex]
7. So, the solution to the system of equations is:
[tex]\[
x = 7, \quad y = 4
\][/tex]
Therefore, the values of [tex]\( x \)[/tex] and [tex]\( y \)[/tex] are [tex]\( x = 7 \)[/tex] and [tex]\( y = 4 \)[/tex].
