Question

5. Jennifer's school is selling tickets to the annual dance

competition. On the first day of ticket sales the school sold 2 senior
citizen tickets and 7 student tickets for a total of $40. On the second
day by selling 8 senior citizen tickets and 2 student tickets for a total
of $56.
a.
Define variables:
b. System:
C.
Solve the systems (optional):

Answer 1

Explanation:

Let "x" be the number of senior tickets and "y" be the number of student tickets.

1st day: 2x + 7y = 40

2nd day: 8x + 2y = 56

(I am going to solve this by elimination and using addition because I find that easier.)

First, we are going to get rid of "y":

2 (2x + 7y = 40) -7 (8x + 2y = 56)

= 4x + 14y = 80 = -56x - 14y = -392

( We multiply the second equation by "-7" so that we can cancel "y")

Now add the equations:

4x + 14y = 80

-56x - 14y = -392

= - 52x = -312

Now divide -312 by -52

= x = 6

Now subsitute 6 in for "x" in the first equation:

2(6) + 7y = 40

= 12 + 7y = 40

Subtract 12 from each side:

= 7y = 28

Divide 7 from each side:

= y = 4

Answer:

x = 6

y = 4

Hope that helps! :D