To determine how many years Nikhil and Mae have been employed by the company, we'll follow a step-by-step approach to solve the given system of equations:
[tex]\[
\begin{array}{l}
x = 4y \\
x = 8 + 2y
\end{array}
\][/tex]
1. Identify the Equations: We have two equations:
- [tex]\( x = 4y \)[/tex] (Equation 1)
- [tex]\( x = 8 + 2y \)[/tex] (Equation 2)
2. Substitute Equation 1 into Equation 2: Since Equation 1 states [tex]\( x = 4y \)[/tex], we can substitute [tex]\( 4y \)[/tex] for [tex]\( x \)[/tex] in Equation 2:
[tex]\[
4y = 8 + 2y
\][/tex]
3. Solve for [tex]\( y \)[/tex]: Now we will isolate [tex]\( y \)[/tex]:
[tex]\[
4y - 2y = 8
\][/tex]
Simplify the left side:
[tex]\[
2y = 8
\][/tex]
Divide both sides by 2:
[tex]\[
y = 4
\][/tex]
4. Determine [tex]\( x \)[/tex] from [tex]\( y \)[/tex]: Now that we have the value of [tex]\( y \)[/tex], substitute it back into Equation 1 to find [tex]\( x \)[/tex]:
[tex]\[
x = 4y
\][/tex]
Substitute [tex]\( y = 4 \)[/tex]:
[tex]\[
x = 4 \times 4 = 16
\][/tex]
5. Conclusion:
- Mae has been employed for [tex]\( y = 4 \)[/tex] years.
- Nikhil has been employed for [tex]\( x = 16 \)[/tex] years.
Therefore, the correct answer is:
Nikhil has been with the company for 16 years, while Mae has been there for 4 years.
