General Maths: Unit 1 Linear Algebra

2A – Substitution Linear Algebra Using the calculator to solve substitution problems…. example “ | ” sign is found under: keyboard  mth  OPTN

Now do: Exercise 2A - Substitution Questions 1a, 2, 3b, 4c, 5b, 6b, 7c, 8a, 9a, 10a

One and Two Step Equations

2C – Solving Equations Linear Algebra Using the calculator to solve…. example one example two – showing working One and Two Step Equations Solve is found on the calculator…. MATH  CALC  solv

2C - Solving Equations Linear Algebra Now do: Worksheet Page One: One and Two Step Equations One and Two Step Equations

Problems involving brackets and grouping like terms

2C - Solving Equations Linear Algebra Worksheet: Exercise 2 – Bracket & Bridging Problems (back page of last worksheet) Complete Exercise 2C – Questions 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25 Problems involving brackets and grouping like terms Now do:

Developing Formulas Linear Algebra Forming equations for Perimeters of shapes How can we write an equation to find the perimeter of: Perimeter = = (5 x 4) = 20

Developing Formulas Linear Algebra Forming equations for Perimeters of shapes How can we write an equation to find the perimeter of…… P = a + a + b + b = 2a + 2b

Now do: Exercise 2D – Questions 1a, 1d, 2, 3, 4, 5, 6, 7 Developing Formulas Linear Algebra

Now do: Exercise 2F – Questions Developing Formulas Linear Algebra

Simultaneous Equations: A set of two equations Both equations have the same two unknowns We can solve simultaneous equations using a few different methods Graphically – Plotting both equations on the same graph and finding where the two lines intersect (Point of Intersection). Algebraically - Substitution Method Elimination Method We will look at the Algebraic Methods a little later. Solving Simultaneous Linear Algebra Equations

Solving Simultaneous Linear Algebra Equations

Solving Simultaneous Linear Algebra Equations

Solving Simultaneous Linear Algebra Equations

Solving Simultaneous Linear Algebra Equations

Solving Simultaneous Linear Algebra Equations

Solving Simultaneous Linear Algebra Equations

Graphically You try: Exercise 2I – 1, 2a, 2c, 2e, 2g, 2i Then: Worksheet – Solving using graphs Solving Simultaneous Linear Algebra Equations

So we can write our solution as (2, 0)

So we can write our solution as (4, 11)

Solving Simultaneous Linear Algebra Equations Substitution You try: Substitution Worksheet

SSS RULE: Signs Same Subtract The signs in front of the ‘3’s are not the same, so we ADD the 2 equations

SSS RULE: Signs Same Subtract The signs in front of the ‘4’s are the same so we SUBTRACT the 2 equations.

X 3 X 2 X 3 X 2 SSS RULE: Signs Same Subtract The signs in front of the ‘6’s are the same so we SUBTRACT the 2 equations. hole We multiply the whole equation by this number

X 3 X 1 X 3 X 1 SSS RULE: Signs Same Subtract The signs in front of the ‘3’s are the same so we SUBTRACT the 2 equations. So our solution is (3, -2)

Solving Simultaneous Equations Elimination Now you try: Elimination Worksheet Then: Exercise 2J – Choose the appropriate method – Substitution or Elimination

Solving Simultaneous Equations Using your calculator

Solving Simultaneous Equations Using your calculator You Try: Exercise 2K

Solving Simultaneous Equations Solving Worded problems using Simultaneous Equations Simultaneous equations are used to solve a variety of problems containing more than one unknown. Eg. Two hamburgers and a packet of chips cost $8.20. One hamburger and Two packets of chips cost $5.90. Find how much one packet of chips and one hamburger costs. 1. Identify Variables 2. Set 2 equations by forming equations from the sentences 3. Solve the equations using substitution, elimination or graphical methods 4. Interpret your answer by referring back to the original question

Solving Simultaneous Equations Solving Worded problems using Simultaneous Equations Eg. Two hamburgers and a packet of chips cost $8.20. One hamburger and Two packets of chips cost $5.90. Find how much one packet of chips and one hamburger costs. 1. Identify Variables 2. Set 2 equations by forming equations from the sentences 3. Solve the equations using any method 4. Interpret your answer by referring back to the original question A hamburger costs $3.50 A packet of chips costs $1.20 Let x = A Hamburger Let y = A packet of Chips 2x + y = 8.20 x + 2y = 5.90

Solving Simultaneous Equations Solving Worded problems using Simultaneous Equations You Try: Worded Problems Worksheet Then: Exercise 2L