Sure! Let's solve the system of equations step-by-step:
[tex]\[
\left\{\begin{array}{c}
2x + y = 11 \\
y = x + 2 \\
\end{array}\right.
\][/tex]
1. Substitute [tex]\( y \)[/tex] from the second equation into the first equation:
The second equation gives us:
[tex]\[
y = x + 2
\][/tex]
Substituting this expression for [tex]\( y \)[/tex] into the first equation:
[tex]\[
2x + (x + 2) = 11
\][/tex]
2. Simplify and solve for [tex]\( x \)[/tex]:
Combine like terms:
[tex]\[
2x + x + 2 = 11
\][/tex]
Simplify:
[tex]\[
3x + 2 = 11
\][/tex]
Subtract 2 from both sides:
[tex]\[
3x = 9
\][/tex]
Divide by 3:
[tex]\[
x = 3
\][/tex]
3. Substitute [tex]\( x = 3 \)[/tex] back into the second equation to find [tex]\( y \)[/tex]:
Using the second equation [tex]\( y = x + 2 \)[/tex]:
[tex]\[
y = 3 + 2
\][/tex]
Simplify:
[tex]\[
y = 5
\][/tex]
So, the solution to the system of equations is:
[tex]\[
x = 3, \quad y = 5
\][/tex]
Therefore, the solution to the given system of equations is [tex]\((x, y) = (3, 5)\)[/tex].
