Name: 

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

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

Identify two like terms and state how they are related.

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

The first equation of a linear system is 2x + 3y = 52. Choose a second equation to form a linear system with infinite solutions.
i) 2x + 3y = –260      ii) –10x – 15y = –260       iii) –10x + 3y = –260      iv) –10x + 3y = 255

Create a linear system to model this situation:
A collection of nickels and dimes contains four times as many dimes as nickels. The total value of the collection is $20.25.

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.

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.

Write a linear system to model this situation. Then verify which of the given solutions is correct.
A crate of 32 grapefruit has a total mass of 4.648 kg.
When 9 grapefruit are removed, the total mass is 3.622 kg.
Verify the mass of the crate and the average mass of one grapefruit.
A.       B.             C.       D.
i)       The crate has a mass of 1 kg, and the mass of one grapefruit is 114 g.
ii)       The crate has a mass of  1.2 kg, and the mass of one grapefruit is 114.2 g.
iii)       The crate has a mass of  1 kg, and the mass of one grapefruit is 114.2 g.
iv)       The crate has a mass of  1.2 kg, and the mass of one grapefruit is 57 g.

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

Use the graph to solve the linear system:
y = –5x
y + = 2x

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

a) (3, 5.3) b) (5.3, 3) c) ( 5.3, –3) d) (–4, 5.3)

     

Use substitution to solve this linear system.
x = 4 + y
x + 16y = –264 

Use substitution to solve this problem:
The perimeter of a rectangular field is 276 m. The length is 18 m longer than the width.
What are the dimensions of the field?

Use an elimination strategy to solve this linear system.

Model this situation with a linear system:
At a campground, 5 large tanks and 5 small tanks contained 3200 L of drinking water. When one of the small tanks was replaced with a large tank, there was 3400 L of drinking water.

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 equation whose graph intersects the graph of –6x + 3y = 11
exactly once.
i) –6x + 3y = 13
ii) –24x + 12y = 44
iii) –4x + 3y = 11

Determine the number of solutions of the linear system:
2x – 5y = 23
–6x + 15y = 21

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?

A submarine cruises underwater at 20 km/h and on the surface at 30 km/h. The submarine travels a distance of 650 km in 25 h. A linear system that models this situation is:
u + s = 25
20u + 30s = 650
where u represents the time in hours cruising underwater, and s represents the time in hours cruising on the surface.
a)       Graph the linear system above.
b)       Use the graph to solve the problem:

Fill in the each blank below with the correct integer.

System A -____: -____:	System B 7x + 6y = –376 –4x – 6y = 256

           

Use an elimination strategy to solve this linear system.

Model this situation with a linear system:
The perimeter of a rectangle is 234 ft. When its length is doubled, the perimeter increases by 58 ft.

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

Sales clerks at an appliance store have a choice of two methods of payment:
Plan A: $580 every two weeks plus 4.2% commission on all sales
Plan B: $880 every two weeks plus 1.2% commission on all sales
a)       Write a linear system to model this situation.
b)       Graph the linear system in part a.
c)       Use the graph to solve this problem:

Use a substitution strategy to solve the following problem.

Two isosceles triangles have the same base length. The equal sides of one of the triangles
are 3.25 times as long as the equal sides of the other. Find the lengths of the sides of the triangles when their perimeters are 38 cm and 96.5 cm.

a)      Write a linear system to model the situation:
b)       Use substitution to solve the related problem: