Nikhil and Mae work at the same company. Nikhil has been at the company 4 times as long as Mae. Nikhil's time at the company is 8 more than 2 times Mae's time. The following system of equations models the scenario:
x = 4y
x = 8 + 2y
How many years has each person been employed by the company?
Using the first equation, we can substitute 4y for x in the second equation:
4y = 8 + 2y
Simplifying this equation, we get:
2y = 8
y = 4
Therefore, Mae has been employed by the company for 4 years. Using the first equation, Nikhil has been employed for 4 times as long, or 4 x 4 = 16 years.
To solve this system of equations, you can use the substitution method.
Step 1: Start with the first equation x = 4y.
Step 2: Substitute x in the second equation with 4y from the first equation:
4y = 8 + 2y.
Step 3: Simplify the equation by subtracting 2y from both sides:
2y = 8.
Step 4: Divide both sides of the equation by 2:
y = 4.
Step 5: Substitute the value of y back into the first equation:
x = 4 * 4 = 16.
Therefore, Nikhil has been employed by the company for 16 years, and Mae has been employed for 4 years.