Certainly! Let's solve the given system of equations step-by-step:
1. We have the following system of equations:
[tex]\[
\left\{\begin{array}{l}
x + y = 6 \\
x = y + 2
\end{array}\right.
\][/tex]
2. First, we'll substitute the expression for [tex]\( x \)[/tex] from the second equation into the first equation. The second equation is:
[tex]\[
x = y + 2
\][/tex]
3. Substitute [tex]\( x = y + 2 \)[/tex] into the first equation [tex]\( x + y = 6 \)[/tex]:
[tex]\[
(y + 2) + y = 6
\][/tex]
4. Combine like terms:
[tex]\[
2y + 2 = 6
\][/tex]
5. Isolate [tex]\( y \)[/tex] by subtracting 2 from both sides of the equation:
[tex]\[
2y = 4
\][/tex]
6. Divide both sides by 2 to solve for [tex]\( y \)[/tex]:
[tex]\[
y = 2
\][/tex]
7. Now substitute [tex]\( y = 2 \)[/tex] back into the second equation [tex]\( x = y + 2 \)[/tex]:
[tex]\[
x = 2 + 2
\][/tex]
8. Simplify to find [tex]\( x \)[/tex]:
[tex]\[
x = 4
\][/tex]
Therefore, the solution to the system of equations is [tex]\( (4, 2) \)[/tex].
So, the correct answer is:
[tex]\[
(4, 2)
\][/tex]
