Name: 

Which linear system has the solution x = –2 and y = 6?

At a skating rink, admission is $4.00 for a student and $8.00 for an adult.
Tuesday evening, 20 people used the skating rink and a total of $132 in admission fees was collected. A linear system that models this situation is:
4s + 8a = 132               
s + a = 20                 
where s represents the number of student admissions, and a represents the number of adult admissions purchased.
Use the graph to solve this problem:
How many students used the skating rink on Tuesday evening?





     

Use the table of values to determine the solution of this linear system:
                       

Write an equivalent linear system where both equations have the same y-coefficients.

The first equation of a linear system is 8x + 13y = 166. Choose a second equation to form a linear system with exactly one solution.
i) 8x + 13y = –830      ii) –40x – 65y = –830       iii) –40x + 13y = –830      iv) –40x – 65y = 0

Create a linear system to model this situation:
A woman is 3 times as old as her son. In thirteen years, she will be 2 times as old as her son will be.

Create a linear system to model this situation:
A length of outdoor lights is formed from strings that are 5 ft. long and 11 ft. long. Fourteen strings of lights are 106 ft. long.

Create a linear system to model this situation:
A rectangular field is 35 m longer than it is wide. The length of the fence around
the perimeter of the field is 290 m.

Yoshiko used this linear system to represent a situation involving the costs of shirts and pants.
3s + p = 144
4s + 3p = 122
What problem might Yoshiko have solved?

A.       Three shirts and one pair of pants cost $144. Four shirts and three pairs of pants cost $122.
B.       Three shirts and one pair of pants cost $144. Two shirts and three pairs of pants cost $122.
C.       Three shirts cost $144. Four shirts and three pairs of pants cost $122.
D.       Three shirts and 4 pairs of pants cost $144. Four shirts and three pairs of pants cost $122.

Use the graph to solve the linear system:
y = –3x – 5
y = 3x      

Determine the solution of the linear system represented by this graph.

a) (2, 3.8) b) (3.8, 2) c) (–3, 3.8) d) (–2, 3.8)

     

Use substitution to solve this problem:
Tanukah invested a total of $4350 in two bonds. He invested in one bond at an annual interest rate of 6% and in another bond at an annual interest rate of 8%. After one year, the total interest earned was $324.00. How much money did Tanukah invest in each bond?

Use an elimination strategy to solve this linear system.

Use an elimination strategy to solve this linear system.

Model this situation with a linear system:
Nate borrowed $10 000 for his university tuition. He borrowed part of the money at an annual interest rate of 2.4% and the rest of the money at an annual interest rate of 4.5%. His total annual interest payment is $250.50.

Without graphing, determine the slope of the graph of the equation:
3x + 4y = 11

Determine the number of solutions of the linear system:
14x + 7y = 315
16x – 2y = 610

Determine the number of solutions of the linear system:
5x + 7y = 76
–25x – 35y = –380

Determine the number of solutions for the linear system that models this problem:

Two people are playing a game. The difference in their points is 83. When the number of points each player has is doubled, the difference is 166. How many points does each person have?

For what value of k does the linear system below have infinite solutions?
x + y = 14
kx + 2y = 28

Create a linear system to model this situation:
The cost of admission to the museum is $5.50 for adults and $3.50 for students.
Yesterday, 100 admissions were sold, and the receipts were $424.00.

a)       Write a linear system to model this situation:
b)       Use a graph to solve this problem:

Create a linear system to model this situation. Then use substitution to solve the linear system to solve the problem.

At the local fair, the admission fee is $8.00 for an adult and $4.50 for a youth. One Saturday, 209 admissions were purchased, with total receipts of $1304.50. How many adult admissions and how many youth admissions were purchased?

Use an elimination strategy to solve this linear system.

Determine the number of solutions of this linear system.
7x – 3y = 43
7x – 3y = 13

a)       Write a linear system to model this situation.
b)      Use a graph to solve this problem:

a)       Use graphing technology to determine the solution of this linear system.
b)       Verify the solution.

a)       Write a linear system to model this situation:
b)       Use graphing technology to solve this problem:
c)      Verify the solution.

Explain what happens when you try to solve this linear system using an elimination strategy. What does this tell you about the graphs of these equations?