Applications
Work through the following word problems carefully.

The matinee ticket price of the movie in Cinema 1 is $5. The matinee ticket price of the movie in Cinema 2 is $7. Your group of 10 people spent $62 on tickets. How many people attended Cinema 1, and how many people attended Cinema 2?
Let x = number of persons attending Cinema 1.
Let y = number of persons attending Cinema 2.
The total number of people in the group is 10, so one equation would be:
x + y = 10
The total spent on ticket prices was $62, so the other equation would be:
5x + 7y = 62
The system of equations that you would use to solve this problem is:
x + y = 10
5x + 7y = 62
Solve the system graphically.

A college Spanish class is planning a trip to Mexico during spring break. At least 12 people must sign up for the trip, or it will be canceled. The number of seniors in the group must not be more than twice the number of juniors. What is the least number of juniors that can be in the group?
Let x = number of juniors going.
Let y = number of seniors going.
There must be at least 12 in the group, so x + y ≥ 12.
The number of seniors must not outnumber the juniors by more than twice as much, so 2x ≤ y.
The system of equations that would solve the problem is:
x + y ≥ 12
2x ≤ y
Graph the system of inequalities to solve the problem.
Solutions
 yes
 yes
 yes
 no
 no
 yes
 no
 no
 no
 yes

y = 2x + 4
y = 3x + 3

y = 2x + 2

y = –4x + 1
y = 4x – 1

2y + 3x = 12 6y – 2x = 4

5y – 10x = 15 (y = 2x + 3) 7y + 14x = 21 (y = –2x + 3)

9x – 3y = 18 (y = 3x + ^{–}6) –4x – y = 10 (y = –4x + 10)

–28x + 4y = 32 (y = 7x + 8) 16x – 16y = –48 (y = x + 3)

–9x + 6y = 12 30x – 15y = 15 (y = 2x + ^{–}1)

200y – 400x = –600 (y = 2x + –3) 75y + 150x = 300 (y = –2x + 4)

–17x – 17y = 17 (y = –x + ^{–}1) –19x – 19y = 19 (y =–x + ^{–1)} (There is an infinite number of solutions to this system.)
 Ø
 infinite
 one
 one
 Ø
 one
 infinite
 Ø















You need four $5 tickets and six $7 tickets.
 You need at least four seniors in the group.
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2
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