Question

What is the solution to the system of equations representing the school athletic director's purchases?

(10x + 5y = 703.55)
(18.50x + 11.99y = 703.55)
a) (15, 22, 18)
b) (14, -20, 21)
c) (15, 22, -18)
d) (14, 20, 21)

Answer 1

The solution to the system of equations representing the school athletic director's purchases is (14.515, 111.68).

Step-by-step explanation:

To find the solution to the system of equations, we can use the method of substitution or elimination. Let's first use the method of substitution:

From the first equation, we can express one variable in terms of the other. Let's solve for x:

10x + 5y = 703.55 --> 10x = 703.55 - 5y --> x = (703.55 - 5y)/10

Now we substitute this expression for x into the second equation:

18.50((703.55 - 5y)/10) + 11.99y = 703.55

Solving for y:

12910.45 - 92.50y + 11.99y = 7035.50 - 59.95y + 11.99y --> 52.51y = 5874.95 --> y = 111.68

Now substitute this value of y back into the first equation to find x:

10x + 5(111.68) = 703.55 --> 10x + 558.40 = 703.55 --> 10x = 145.15 --> x = 14.515

Therefore, the solution to the system of equations is (14.515, 111.68).