Student tickets to the Homecoming game cost $5 each. General admission tickets cost $8 each. So far, 150 tickets have been sold. $900 has been collected. A. Write a system of equations for this model in standard form?
B. What is the solution to the system?

For purposes of this exercise,

x

represents the number homecoming tickets, and

y

represents the number of general admission sold.

A-The system of equations is:

x

+

y

=

150

5

x

+

8

y

=

900

B- Attachment

C- Let's solve this system of equations by elimination.

x

+

y

=

150

5

x

+

8

y

=

900

The first step will be multiply the first equation for -5, we will have

−

5

x

+

−

5

y

=

−

750

5

x

+

8

y

=

900

If we add both equations

x

will be eliminated and the new equation will be:

3

y

=

150

y

=

50

Replacing the value of

y

on the first equation, we have:

x

+

50

=

150

x

=

100

The solution is

(

100

,

50

)

D- To be a solution for the system of equations, it should be a solution for each equation in the system. Plugging

x

and

y

values in the first equation

x

+

y

=

150

180

−

30

=

150

s

o

l

u

t

i

o

n

For the second equation:

5

x

+

8

x

=

900

5

∗

180

+

8

(

−

30

)

=

900

900

−

240

≠

900

y

represents the number of tickets for general admissions, the numbers of tickets should not be a negative number.