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## LINEAR EQUATIONS

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**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 linear equations**If thepronumeralappears 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.**Substitution and transposition in linear relations**Complete the following table using the CAS calculator**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**Find a difference equation which describes this situation**Write the corresponding linear equation and set up a table of values**Write the linear equation for the costs of making the**candles. Write the linear equation for selling the candles. Set up a table of values for both equations using your CAS calculator 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**Solve the following simultaneous equations**using the substitution method using the CAS calculator**Solving problems using simultaneous equations**• 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 = 8.20 x + 2y = 5.90**5x + 2y = 149.69**3x + 3y = 134.70 3.5x + 5.2y = 799.60 x + 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 113 MC: Q1, 2, 3, 4, 5, 6, 9, 12, 13, 15, 17, 18, 24 SHORT ANSWER: Q1, 5, 6, 8 EXTENDED RESPONSE: Q1(a,b,c), 3 eBook plus ACTIVITIES p118