Name: 

Identify two like terms and state how they are related.
–10x + 20y = 460
30x + 60y = 1620

For each equation, identify a number you could multiply each term by to ensure that the coefficients of the variables and the constant term are integers.
(1)      x + y =            
(2)       x – y =            

Write an equivalent system with integer coefficients.
x + y =                      
x + 5y =                

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

Use substitution to solve this linear system.
x = 2y – 56     
5x + 13y = 410

Use substitution to solve this linear system:
x – y = 18
x + y =

The solution of this linear system is (–28, y). Determine the value of y.
x – y =                      
x – 4y =      

Use an elimination strategy to solve this linear system.

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:
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.

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

Without graphing, determine which of these equations represent parallel lines.
i) –6x + 6y = 12
ii) –4x + 6y = 12
iii) –2x + 6y = 12
iv) –6x + 6y = 14

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:
14x + 7y = 315
16x – 2y = 610

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

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

Fill in the each blank below with the correct integer.

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

           

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

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

Determine the number of solutions of this linear system.
15x + 30y = –240
17x + 21y = 53

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

Use a substitution strategy to solve the following problem.

Vivian invested a total of $5600 in two bonds. She invested in one bond at 2% per annum and in another bond at 5% per annum. In one year, the interest earned on each bond was the same. How much did Vivian invest in each bond?

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.

Explain what happens when you try to solve this linear system using a substitution strategy. What does this indicate about the graphs of these equations?

Determine the number of solutions of this linear system.