LINEAR EQUATIONS

A linear equation is an equation which contains a pronumeral raised to the power

of 1

Solving linear equations

• To solve a linear equation we have to find a value of the pronumeral which makes the equation a true statement.

 • It is solved in the reverse order that

the equation is built up.

SOLVING EQUATIONS

Solving linear equations

If the pronumeral appears in the equation more than once, we must collect terms containing the unknown on one side of the equation and all the other terms on the other side.

Solving equations with brackets

If the equation contains brackets, they should be expanded first

OR

Divide both sides of the equation by the coefficient in front of the brackets

Solving equations containing fractions

How many terms are there in the above equation?

What is the denominator of each term?

What is the lowest common denominator (LCD)?

How many terms are there in the above equation?

What is the denominator of each term?

What is the lowest common denominator (LCD)?

Solving problems using linear equations

The price of coffee rose by 20% and is now $4.80 a jar. Find the cost of the same jar before the price rise.

Solving equations on the CAS calculator

p.75

Substitution and transposition in linear relations

Complete the following table using the CAS calculator

Celsius Fahrenheit

0

5

10

15

20

25

30

Transposing formulas on the CAS calculator

p.88

Difference equations and corresponding linear equations

“a” is the first term and “d” is the difference between each term.

Find the difference equation and corresponding linear equation for the following tables of values

a) Find a difference equation which describes this situation

b) Write the corresponding linear equation and set up a

table of values

a) Write the linear equation for the costs of making the candles.

b) Write the linear equation for selling the candles.

c) Set up a table of values for both equations using your CAS calculator

d) How many candles have to be sold before a profit is made?

Use the graphical method to solve the simultaneous equations

y = 1.2x + 15 and y = 3.5x

Graphing simultaneous equations on the CAS calculator

p.100

Solve the following simultaneous equations a) using the substitution methodb) using the CAS calculator

Solving problems using simultaneous equations

1. Identify the variables

2. Set up simultaneous equations by transforming written information into algebraic sentences

3. Solve the equations by using the graphical method or substitution

Two hamburgers and a packet of chips cost $8.20, while 1 hamburger and 2 packets of chips cost $5.90.

Find the cost of a packet of chips and a hamburger.

2x + y = 8.20x + 2y = 5.90

Solving simultaneous equations on the CAS calculator

p.104

5x + 2y = 149.693x + 3y = 134.70

3.5x + 5.2y = 799.60x + y = 193

SUMMARY TOPICS p112

• LINEAR EQUATIONS• SOLVING PROBLEMS WITH LINEAR EQUATIONS• SUBSTITUTION AND TRANSPOSING FORMULAS• LINEAR RECURSIVE RELATIONSHIPS• SIMULTANEOUS EQUATIONS• SOLVING PROBLEMS USING SIMULTANEOUS EQUATIONS

Include instructions on how to use the CAS calculator

CHAPTER REVIEW QUESTIONS P 113MC: Q1, 2, 3, 4, 5, 6, 9, 12, 13, 15, 17, 18, 24SHORT ANSWER: Q1, 5, 6, 8EXTENDED RESPONSE: Q1(a,b,c), 3

eBook plus ACTIVITIES p118