Grade 10 Mathematics Page 1 of 3

Final Exam Review (Unit 1) Date:

RHHS Mathematics Department

Unit 1: Linear Systems

Solving Linear Systems Graphically

To solve the following system by graphing, write the equations in the

slope and y-intercept form.

(2) 22

(1) 83

yx

yx

Graph the equations. Find the point of intersection.

Solving Linear Systems by Substitution

To solve the following system by substitution, solve one equation for a variable that has a coefficient of 1 or

-1, and then substitute in the second equation.

(2) 523

(1) 22

yx

yx

Solving Linear Systems by Elimination

To solve by elimination, multiply one or both equations by numbers to obtain two equations in which the

coefficients of one variable are the same or opposites.

(2) 625

(1) 1032

yx

yx

Grade 10 Mathematics Page 2 of 3

Final Exam Review (Unit 1) Date:

RHHS Mathematics Department

Solving Problems using Linear Systems

To solve a problem using a linear system,

a) Read the problem carefully, identify the unknowns, and assign variables to the unknowns.

b) Determine how the unknowns are related

c) Write a system of equations that shows relationships between the unknowns

d) Solve the system of equations

e) Check the solution, using the facts given in the problem.

Refer to the lessons and the course pack for examples to review.

Review Exercise: Unit 1

1. Create and solve a linear system of equations that models the following problems. Show a proper

solution including let statements and closing sentences.

a) Bart’s cell phone package costs $15 a month with an additional charge of $0.10 per minute.

Lisa’s pays $10 a month plus $0.12 per minute. When would their monthly bills be the same?

b) Frasier invested $1200 in an RRSP. He invested part of the money in a technology fund that pays

interest at 15% per year. He puts the remainder in savings bonds that pay 5% interest per year.

If he earned $160 in interest in one year, how much did he invest in each fund?

2. Solve the following system graphically: 1243

82

yx

xy

3. Solve the following system using elimination:

1354

5886

yx

yx

4. For the following system of equations, determine, without solving, the number of solutions the system

has:

18315

122

yx

yx

5. Evaluate ba 23 if 3

2,

2

1 ba .

6. Solve each of the following:

74)1(2) yyya 45

213

4

1) xxb

7. Which of the following points lie on the line 43

2 xy :

)2,3() Aa )2,3() Bb )0,6() Cc

3

2,5)d

Chapter 1 Review: P. 119 #1,2,4,12,13,15–23,25.

Grade 10 Mathematics Page 3 of 3

Final Exam Review (Unit 1) Date:

RHHS Mathematics Department

Answers – Chapter 1:

1. a) The cell phone plans cost the same when 250 minutes of calls are placed. The cost is $40.00.

b) He invested $1000 in the technology fund and $200 in savings bonds.

2. 3. The solution is )5,3(),( yx .

4. Since their slopes are different, there will

be one solution.

5. 12

1

The point of intersection is )0,4( . 6. 7

37)9) xbya

7. A and C