Solve each system of linear equation and explain any method you used:
-A company produces telephones at the rate of 600 per day. A customer survey indicates that the demand for phones with built in answering machines is twice as great as the demand for phones without the machines. If you are deciding the production quota for the day, how many phones with answering machines would you schedule for production? How many without
Let's assume the number of phones without answering machines is "x" and the number of phones with answering machines is "y".
According to the information provided, the demand for phones with answering machines is twice as great as the demand for phones without answering machines. This can be expressed as:
y = 2x (Equation 1)
The company produces telephones at a rate of 600 per day. So, the total number of phones produced should be equal to the sum of phones with answering machines and phones without answering machines:
x + y = 600 (Equation 2)
To solve this system of equations, we can use substitution method or elimination method. Let's use substitution method:
From Equation 1, we can substitute the value of y in Equation 2:
x + 2x = 600
3x = 600
x = 200
Now, substituting the value of x back into Equation 1:
y = 2x
y = 2(200)
y = 400
So, the optimal production quota for the day would be 400 phones with answering machines and 200 phones without answering machines.