To solve the system of equations:
[tex]\[
\begin{cases}
2x + y = 18 \\
y = 2x - 10
\end{cases}
\][/tex]
we can follow these steps:
1. Substitute [tex]\(y\)[/tex] from the second equation into the first equation:
We know from the second equation that [tex]\(y = 2x - 10\)[/tex]. Substitute this expression for [tex]\(y\)[/tex] into the first equation:
[tex]\[
2x + (2x - 10) = 18
\][/tex]
2. Combine like terms and solve for [tex]\(x\)[/tex]:
Combine the terms involving [tex]\(x\)[/tex]:
[tex]\[
2x + 2x - 10 = 18 \\
4x - 10 = 18
\][/tex]
Add 10 to both sides to isolate the term with [tex]\(x\)[/tex]:
[tex]\[
4x = 28
\][/tex]
Divide both sides by 4:
[tex]\[
x = 7
\][/tex]
3. Substitute [tex]\(x\)[/tex] back into the second equation to find [tex]\(y\)[/tex]:
We know [tex]\(x = 7\)[/tex]. Substitute this value back into the second equation [tex]\(y = 2x - 10\)[/tex]:
[tex]\[
y = 2(7) - 10 \\
y = 14 - 10 \\
y = 4
\][/tex]
Thus, the solution to the system of equations is:
[tex]\[
x = 7, \quad y = 4
\][/tex]
Therefore, the solution to the system of equations is [tex]\((x, y) = (7, 4) \)[/tex].
