Simultaneous Equations S4 General Solving Sim. Equations Graphically Graphs as Mathematical Models Solving Simple Sim. Equations by Substitution www.mathsrevision.com Solving Simple Sim. Equations by elimination Solving harder type Sim. equations 18-Feb-19 Created by Mr. Lafferty Maths Department

Created by Mr. Lafferty Maths Department Starter Questions S4 General www.mathsrevision.com 18-Feb-19 Created by Mr. Lafferty Maths Department

Created by Mr. Lafferty Maths Department Simultaneous Equations S4 General Straight Lines Learning Intention Success Criteria To solve simultaneous equations using graphical methods. Interpret information from a line graph. Plot line equations on a graph. 3. Find the coordinates were 2 lines intersect ( meet) www.mathsrevision.com 18-Feb-19 Created by Mr. Lafferty Maths Department

Created by Mr. Lafferty Maths Department Q. Find the equation of each line. (1,3) Q. Write down the coordinates were they meet. 18-Feb-19 Created by Mr. Lafferty Maths Department

Created by Mr. Lafferty Maths Department Q. Find the equation of each line. Q. Write down the coordinates where they meet. (-0.5,-0.5) 18-Feb-19 Created by Mr. Lafferty Maths Department

Created by Mr. Lafferty Maths Department Q. Plot the lines. (1,1) Q. Write down the coordinates where they meet. 18-Feb-19 Created by Mr. Lafferty Maths Department

Created by Mr. Lafferty Maths Department Now try Exercise 2 Ch7 (page 84 ) www.mathsrevision.com 18-Feb-19 Created by Mr. Lafferty Maths Department

Created by Mr. Lafferty Maths Department Starter Questions S4 General 8cm www.mathsrevision.com 5cm 18-Feb-19 Created by Mr. Lafferty Maths Department

Created by Mr. Lafferty Maths Department Simultaneous Equations S4 General Straight Lines Learning Intention Success Criteria To use graphical methods to solve real-life mathematical models Draw line graphs given a table of points. 2. Find the coordinates were 2 lines intersect ( meet) www.mathsrevision.com 18-Feb-19 Created by Mr. Lafferty Maths Department

Created by Mr. Lafferty Maths Department We can use straight line theory to work out real-life problems especially useful when trying to work out hire charges. Q. I need to hire a car for a number of days. Below are the hire charges charges for two companies. Complete tables and plot values on the same graph. 160 180 200 180 240 300 18-Feb-19 Created by Mr. Lafferty Maths Department

Who should I hire the car from? Summarise data ! Who should I hire the car from? Total Cost £ Arnold Swinton Up to 2 days Swinton Over 2 days Arnold Days 18-Feb-19 Created by Mr. Lafferty Maths Department

Created by Mr. Lafferty Maths Department Key steps 1. Fill in tables 2. Plot points on the same graph ( pick scale carefully) 3. Identify intersection point ( where 2 lines meet) 4. Interpret graph information. 18-Feb-19 Created by Mr. Lafferty Maths Department

Created by Mr. Lafferty Maths Department Now try Exercise 3 Ch7 (page 85 ) www.mathsrevision.com 18-Feb-19 Created by Mr. Lafferty Maths Department

Created by Mr. Lafferty Maths Department Starter Questions S4 General www.mathsrevision.com 18-Feb-19 Created by Mr. Lafferty Maths Department

Created by Mr. Lafferty Maths Department Simultaneous Equations S4 General Straight Lines Learning Intention Success Criteria To solve pairs of equations by substitution. 1. Apply the process of substitution to solve simple simultaneous equations. www.mathsrevision.com 18-Feb-19 Created by Mr. Lafferty Maths Department

Created by Mr. Lafferty Maths Department Example 1 Solve the equations y = 2x y = x+1 by substitution 18-Feb-19 Created by Mr. Lafferty Maths Department

Created by Mr. Lafferty Maths Department At the point of intersection y coordinates are equal: y = 2x y = x+1 so we have 2x = x+1 Rearranging we get : 2x - x = 1 x = 1 Finally : Sub into one of the equations to get y value y = 2x = 2 x 1 = 2 OR y = x+1 = 1 + 1 = 2 The solution is x = 1 y = 2 or (1,2) 18-Feb-19 Created by Mr. Lafferty Maths Department

Created by Mr. Lafferty Maths Department Example 1 Solve the equations y = x + 1 x + y = 4 by substitution (1.5, 2.5) 18-Feb-19 Created by Mr. Lafferty Maths Department

Created by Mr. Lafferty Maths Department The solution is x = 1.5 y = 2.5 (1.5,2.5) At the point of intersection y coordinates are equal: so we have x+1 = -x+4 y = x +1 y =-x+ 4 2x = 4 - 1 Rearranging we get : 2x = 3 x = 3 ÷ 2 = 1.5 Finally : Sub into one of the equations to get y value y = x +1 = 1.5 + 1 = 2.5 OR y = -x+4 = -1.5 + 4 = 2 .5 18-Feb-19 Created by Mr. Lafferty Maths Department

Created by Mr. Lafferty Maths Department Now try Ex 4 Ch7 (page88 ) www.mathsrevision.com 18-Feb-19 Created by Mr. Lafferty Maths Department

Created by Mr. Lafferty Maths Department Starter Questions S4 General www.mathsrevision.com 18-Feb-19 Created by Mr. Lafferty Maths Department

Created by Mr. Lafferty Maths Department Simultaneous Equations S4 General Straight Lines Learning Intention Success Criteria To solve simultaneous equations of 2 variables. Understand the term simultaneous equation. Understand the process for solving simultaneous equation of two variables. 3. Solve simple equations www.mathsrevision.com 18-Feb-19 Created by Mr. Lafferty Maths Department

Created by Mr. Lafferty Maths Department Example 1 Solve the equations x + 2y = 14 x + y = 9 by elimination 18-Feb-19 Created by Mr. Lafferty Maths Department

Created by Mr. Lafferty Maths Department Step 1: Label the equations x + 2y = 14 (A) x + y = 9 (B) Step 2: Decide what you want to eliminate Eliminate x by subtracting (B) from (A) x + 2y = 14 (A) x + y = 9 (B) y = 5 18-Feb-19 Created by Mr. Lafferty Maths Department

Created by Mr. Lafferty Maths Department Step 3: Sub into one of the equations to get other variable Substitute y = 5 in (B) x + y = 9 (B) x + 5 = 9 x = 9 - 5 The solution is x = 4 y = 5 x = 4 Step 4: Check answers by substituting into both equations x + 2y = 14 x + y = 9 ( 4 + 10 = 14) ( 4 + 5 = 9) 18-Feb-19 Created by Mr. Lafferty Maths Department

Created by Mr. Lafferty Maths Department Example 2 Solve the equations 2x - y = 11 x - y = 4 by elimination 18-Feb-19 Created by Mr. Lafferty Maths Department

Created by Mr. Lafferty Maths Department Step 1: Label the equations 2x - y = 11 (A) x - y = 4 (B) Step 2: Decide what you want to eliminate Eliminate y by subtracting (B) from (A) 2x - y = 11 (A) x - y = 4 (B) x = 7 18-Feb-19 Created by Mr. Lafferty Maths Department

Created by Mr. Lafferty Maths Department Step 3: Sub into one of the equations to get other variable Substitute x = 7 in (B) x - y = 4 (B) 7 - y = 4 y = 7 - 4 The solution is x =7 y =3 y = 3 Step 4: Check answers by substituting into both equations 2x - y = 11 x - y = 4 ( 14 - 3 = 11) ( 7 - 3 = 4) 18-Feb-19 Created by Mr. Lafferty Maths Department

Created by Mr. Lafferty Maths Department Example 3 Solve the equations 2x - y = 6 x + y = 9 by elimination 18-Feb-19 Created by Mr. Lafferty Maths Department

Created by Mr. Lafferty Maths Department Step 1: Label the equations 2x - y = 6 (A) x + y = 9 (B) Step 2: Decide what you want to eliminate Eliminate y by adding (A) from (B) 2x - y = 6 (A) x + y = 9 (B) 3x = 15 x = 15 ÷ 3 = 5 18-Feb-19 Created by Mr. Lafferty Maths Department

Created by Mr. Lafferty Maths Department Step 3: Sub into one of the equations to get other variable Substitute x = 5 in (B) x + y = 9 (B) 5 + y = 9 y = 9 - 5 The solution is x = 5 y = 4 y = 4 Step 4: Check answers by substituting into both equations 2x - y = 6 x + y = 9 ( 10 - 4 = 6) ( 5 + 4 = 9) 18-Feb-19 Created by Mr. Lafferty Maths Department

Created by Mr. Lafferty Maths Department Now try Ex 5A Ch7 (page89 ) www.mathsrevision.com 18-Feb-19 Created by Mr. Lafferty Maths Department

Created by Mr. Lafferty Maths Department Starter Questions S4 General www.mathsrevision.com 18-Feb-19 Created by Mr. Lafferty Maths Department

Created by Mr. Lafferty Maths Department Simultaneous Equations S4 General Straight Lines Learning Intention Success Criteria To solve harder simultaneous equations of 2 variables. 1. Apply the process for solving simultaneous equations to harder examples. www.mathsrevision.com 18-Feb-19 Created by Mr. Lafferty Maths Department

Created by Mr. Lafferty Maths Department Example 1 Solve the equations 2x + y = 9 x - 3y = 1 by elimination 18-Feb-19 Created by Mr. Lafferty Maths Department

Created by Mr. Lafferty Maths Department Step 1: Label the equations 2x + y = 9 (A) x -3y = 1 (B) Step 2: Decide what you want to eliminate Adding Eliminate y by : 2x + y = 9 x -3y = 1 (A) x3 6x + 3y = 27 (C) x - 3y = 1 (D) (B) x1 7x = 28 x = 28 ÷ 7 = 4 18-Feb-19 Created by Mr. Lafferty Maths Department

Created by Mr. Lafferty Maths Department Step 3: Sub into one of the equations to get other variable Substitute x = 4 in equation (A) 2 x 4 + y = 9 y = 9 – 8 y = 1 The solution is x = 4 y = 1 Step 4: Check answers by substituting into both equations 2x + y = 9 x -3y = 1 ( 8 + 1 = 9) ( 4 - 3 = 1) 18-Feb-19 Created by Mr. Lafferty Maths Department

Created by Mr. Lafferty Maths Department Example 2 Solve the equations 3x + 2y = 13 2x + y = 8 by elimination 18-Feb-19 Created by Mr. Lafferty Maths Department

Created by Mr. Lafferty Maths Department Step 1: Label the equations 3x + 2y = 13 (A) 2x + y = 8 (B) Step 2: Decide what you want to eliminate Subtract Eliminate y by : 3x + 2y = 13 2x + y = 8 (A) x1 3x + 2y = 13 (C) 4x + 2y = 16 (D) (B) x2 -x = -3 x = 3 18-Feb-19 Created by Mr. Lafferty Maths Department

Created by Mr. Lafferty Maths Department Step 3: Sub into one of the equations to get other variable Substitute x = 3 in equation (B) 2 x 3 + y = 8 y = 8 – 6 y = 2 The solution is x = 3 y = 2 Step 4: Check answers by substituting into both equations 3x + 2y = 13 2x + y = 8 ( 9 + 4 = 13) ( 6 + 2 = 8) 18-Feb-19 Created by Mr. Lafferty Maths Department

Created by Mr. Lafferty Maths Department Now try Ex 5B Ch7 (page90 ) www.mathsrevision.com 18-Feb-19 Created by Mr. Lafferty Maths Department