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Summary Template – Module 3 Linear AlgebraUse the following statements to help you create your own summary of the topics covered in Week 3.1.Expanding Brackets (The Distributive Law):a.Complete the equation below showing thegeneral formof the Distributive Law:b.Use the Distributive Law to remove the brackets from the following:1)5x – 52)–gh -4g3)3a2+ 6a2.Linear Equations (1 Variable):a. In general, alinear equation with one variablecan be represented by theGive an example of a specific linear equation with one variable and identify thesimplevariable(the term that can take a range of values) and theconstants(just numbers!)2Y + 3 = 4b.Remembering that to solve an equation, ‘what you do to one side, you must do to theother to keep things balanced’, solve:i.4 k = 40Dividing both sides by 4,4k/4 = 40/4Hence K = 10ii.5 e + 7 = 29 – 6eRearranging the terms,11e = 22Dividing both sides by 11,e = 2.1aa

3.Linear Equations (2 Variables):a.Linear Equations with 2 variablesare often written in ‘Slope-Intercept’form,where andrepresent simple variables and and represent constants. Using these pro-numerals,complete the general form of a linear equation with 2 variables below:Y = 4x + 2b.P=42p = 3q – 78 = 3q-73q = 15Divide both sides by 5,q = 15/3 = 5.4.Simultaneous Equations:a.Simultaneous equationsare solved at the same time as the equations havethe same unknowns..They have the same unknowns.b.There are a number of methods that can be used to solve equations simultaneously. Inyour own words, summarise the steps in theSubstitutionandEliminationMethods.Substitution methods:Step 1:Solve one of the equations for eitherx =ory =.Step 2:Substitute the solution from step 1 into the other equation.Step 3:Solve this new equation.Step 4:Solve for the second variable.Elimination methods:Step 1: Multiply each equation by a suitable number so that the two equations havethe same leading coefficient. ...Step 2: Subtract the second equation from the first.Step 3: Solve this new equation for y.Step 4: Substitute y into either Equation 1 or Equation 2 above and solve forx.2

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