Name: 

Which linear system has the solution x = 4 and y = –2?

Express each equation in slope-intercept form.
x + y = –83
12x + 4y = –1772

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

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

The first equation of a linear system is –6x + 12y = –42. Choose a second equation to form a linear system with no solution.
i) –6x + 12y = 126      ii) 18x – 36y = 126       iii) 18x + 12y = 126      iv) 18x + 36y = 0

Create a linear system to model this situation:
The perimeter of an isosceles triangle is 36 cm. The base of the triangle is 9 cm longer than each equal side.

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 rectangular field is 35 m longer than it is wide. The length of the fence around
the perimeter of the field is 290 m.

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.

Which linear system is represented by this graph?

a)       x – y = 5 5x + 6y = 18 b)      x – y = 7 5x + 6y = 18 c)       x – y = 9 6x + 6y = 18 d)      x – y = 11 6x + 5y = 18

     

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 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:
Frieda has a 13% silver alloy and a 31% silver alloy. Frieda wants to make 26 kg of an alloy that is 47% silver.

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.

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:
2x – 5y = 23
–6x + 15y = 21

Two lines in a linear system have the same slope, but different y-intercepts.
How many solutions does the linear system have?

Solve this linear system by graphing.
–3x – 2y = 16
–x + y = –8

Solve this linear system by graphing.
y = –8
–3x + y = 7

Use graphing technology to solve this linear system.
Where necessary, write the coordinates to the nearest tenth.
–3x + 4y = –3
5x + 6y = –5

Identify two like terms and say how they are related.
6x + 4y = –258
–3x + 5y = 45
     

For what values of k does the linear system below have:
a)      infinite solutions?
b)      one solution?
c)       no solution?

In a piggy bank, the number of nickels is 8 more than one-half the number of quarters. The value of the coins is $21.85.
a)       Create a linear system to model the situation.
b)      If the number of quarters is 78, determine the number of nickels.

These balance scales illustrate the two different sizes of cartons of detergent:
x represents the mass of a large carton and y represents the mass of a small carton.

a)       Write a linear system to model the two balance scales.
c)       Use the linear system to verify the masses of the cartons in part b.

a)       Write a linear system whose solution is: x = 5, y = –5.
b)       Is there more than one linear system with this solution? Explain.

a)       Write a linear system to model the situation:

b)       Solve the linear system by substitution to solve the related 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.