Simultaneous Equations www mathsrevision com S 4 General

Simultaneous Equations www. mathsrevision. com S 4 General Solving Sim. Equations Graphically Graphs as Mathematical Models Solving Simple Sim. Equations by Substitution Solving Simple Sim. Equations by elimination Solving harder type Sim. equations 2/23/2021 Created by Mr. Lafferty Maths Department

Starter Questions www. mathsrevision. com S 4 General 2/23/2021 Created by Mr. Lafferty Maths Department

Simultaneous Equations www. mathsrevision. com S 4 General Straight Lines Learning Intention 1. To solve simultaneous equations using graphical methods. Success Criteria 1. Interpret information from a line graph. 2. Plot line equations on a graph. 3. Find the coordinates were 2 lines intersect ( meet) 2/23/2021 Created by Mr. Lafferty Maths Department

www. mathsrevision. com S 4 General Simultaneous Equations Straight Lines Q. Find the equation of each line. (1, 3) Q. Write down the coordinates were they meet. 2/23/2021 Created by Mr. Lafferty Maths Department

www. mathsrevision. com S 4 General Simultaneous Equations Straight Lines Q. Find the equation of each line. Q. Write down the coordinates where they meet. 2/23/2021 (-0. 5, -0. 5) Created by Mr. Lafferty Maths Department

www. mathsrevision. com S 4 General Simultaneous Equations Straight Lines Q. Plot the lines. (1, 1) Q. Write down the coordinates where they meet. 2/23/2021 Created by Mr. Lafferty Maths Department

www. mathsrevision. com S 4 General Simultaneous Equations Straight Lines Now try Exercise 2 Ch 7 (page 84 ) 2/23/2021 Created by Mr. Lafferty Maths Department

Starter Questions www. mathsrevision. com S 4 General 8 cm 5 cm 2/23/2021 Created by Mr. Lafferty Maths Department

Simultaneous Equations www. mathsrevision. com S 4 General Straight Lines Learning Intention 1. To use graphical methods to solve real-life mathematical models 2/23/2021 Success Criteria 1. Draw line graphs given a table of points. 2. Find the coordinates were 2 lines intersect ( meet) Created by Mr. Lafferty Maths Department

www. mathsrevision. com S 4 General Simultaneous Equations Straight Lines We can use straight line theory to work out real-life problems especially useful when trying to work out hire charges. Q. 2/23/2021 I need to hire a car for a number of days. Below are the hire charges for two companies. Complete tables and plot values on the same graph. 160 180 200 180 240 300 Created by Mr. Lafferty Maths Department

Straight Lines Summarise data ! Who should I hire the car from? Total Cost £ www. mathsrevision. com S 4 General Simultaneous Equations 2/23/2021 d Arnol n o nt i w S Up to 2 days Swinton Over 2 days Arnold Days Created by Mr. Lafferty Maths Department

www. mathsrevision. com S 4 General Simultaneous Equations Straight Lines 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. 2/23/2021 Created by Mr. Lafferty Maths Department

www. mathsrevision. com S 4 General Simultaneous Equations Straight Lines Now try Exercise 3 Ch 7 (page 85 ) 2/23/2021 Created by Mr. Lafferty Maths Department

Starter Questions www. mathsrevision. com S 4 General 2/23/2021 Created by Mr. Lafferty Maths Department

Simultaneous Equations www. mathsrevision. com S 4 General Straight Lines Learning Intention 1. To solve pairs of equations by substitution. 2/23/2021 Success Criteria 1. Apply the process of substitution to solve simple simultaneous equations. Created by Mr. Lafferty Maths Department

S 4 General Simultaneous Equations Straight Lines www. mathsrevision. com Example 1 Solve the equations y = 2 x y = x+1 by substitution 2/23/2021 Created by Mr. Lafferty Maths Department

S 4 General Simultaneous Equations Straight Lines www. mathsrevision. com At the point of intersection y coordinates are equal: y = 2 x y = x+1 2 x = x+1 so we have Rearranging we get : 2 x - x = 1 Finally : Sub into one of the equations to get y value y = 2 x = 2 x 1 = 2 OR The solution is x = 1 2/23/2021 y = x+1 = 1 + 1 = 2 y = 2 or (1, 2) Created by Mr. Lafferty Maths Department

S 4 General Simultaneous Equations Straight Lines www. mathsrevision. com Example 1 Solve the equations (1. 5, 2. 5) y = x + 1 x + y = 4 by substitution 2/23/2021 Created by Mr. Lafferty Maths Department

The solution is x = 1. 5 y = 2. 5 (1. 5, 2. 5) S 4 General Simultaneous Equations Straight Lines www. mathsrevision. com At the point of intersection y coordinates are equal: y = x +1 y =-x+ 4 x+1 Rearranging we get : 2 x 2 x x so we have = = -x+4 4 - 1 3 3 ÷ 2 = 1. 5 Finally : Sub into one of the equations to get y value y = x +1 = 1. 5 + 1 = 2. 5 OR 2/23/2021 y = -x+4 = -1. 5 + 4 = 2. 5 Created by Mr. Lafferty Maths Department

www. mathsrevision. com S 4 General Simultaneous Equations Straight Lines Now try Ex 4 Ch 7 (page 88 ) 2/23/2021 Created by Mr. Lafferty Maths Department

Starter Questions www. mathsrevision. com S 4 General 2/23/2021 Created by Mr. Lafferty Maths Department

Simultaneous Equations www. mathsrevision. com S 4 General Straight Lines Learning Intention 1. To solve simultaneous equations of 2 variables. Success Criteria 1. Understand the term simultaneous equation. 2. Understand the process for solving simultaneous equation of two variables. 3. Solve simple equations 2/23/2021 Created by Mr. Lafferty Maths Department

www. mathsrevision. com S 4 General Simultaneous Equations Straight Lines Example 1 Solve the equations x + 2 y = 14 x + y = 9 by elimination 2/23/2021 Created by Mr. Lafferty Maths Department

www. mathsrevision. com S 4 General Simultaneous Equations Straight Lines Step 1: Label the equations x + 2 y = 14 (A) x + y = 9 (B) Step 2: Decide what you want to eliminate Eliminate x by subtracting (B) from (A) x + 2 y = 14 (A) x + y = 9 (B) y = 5 2/23/2021 Created by Mr. Lafferty Maths Department

S 4 General Simultaneous Equations Straight Lines www. mathsrevision. com 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 x = 4 Step 4: x + 2 y = 14 x + y = 9 2/23/2021 The solution is x = 4 y = 5 Check answers by substituting into both equations ( 4 + 10 = 14) ( 4 + 5 = 9) Created by Mr. Lafferty Maths Department

www. mathsrevision. com S 4 General Simultaneous Equations Straight Lines Example 2 Solve the equations 2 x - y = 11 x - y = 4 by elimination 2/23/2021 Created by Mr. Lafferty Maths Department

www. mathsrevision. com S 4 General Simultaneous Equations Straight Lines Step 1: Label the equations 2 x - y = 11 (A) x - y = 4 (B) Step 2: Decide what you want to eliminate Eliminate y by subtracting (B) from (A) 2 x - y = 11 (A) x - y = 4 (B) x = 7 2/23/2021 Created by Mr. Lafferty Maths Department

S 4 General Simultaneous Equations Straight Lines www. mathsrevision. com 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 y = 3 Step 4: 2 x - y = 11 x - y = 4 2/23/2021 The solution is x =7 y =3 Check answers by substituting into both equations ( 14 - 3 = 11) ( 7 - 3 = 4) Created by Mr. Lafferty Maths Department

www. mathsrevision. com S 4 General Simultaneous Equations Straight Lines Example 3 Solve the equations 2 x - y = 6 x + y = 9 by elimination 2/23/2021 Created by Mr. Lafferty Maths Department

www. mathsrevision. com S 4 General Simultaneous Equations Straight Lines Step 1: Label the equations 2 x - y = 6 (A) x + y = 9 (B) Step 2: Decide what you want to eliminate Eliminate y by adding (A) from (B) 2 x - y = 6 x + y = 9 (A) (B) 3 x = 15 2/23/2021 x = 15 ÷ 3 = 5 Created by Mr. Lafferty Maths Department

S 4 General Simultaneous Equations Straight Lines www. mathsrevision. com Step 3: Sub into one of the equations to get other variable Substitute x = 5 in (B) x + y = 9 (B) 5 + y = 9 - 5 Step 4: y = 4 The solution is x = 5 y = 4 Check answers by substituting into both equations 2 x - y = 6 x + y = 9 2/23/2021 ( 10 - 4 = 6) ( 5 + 4 = 9) Created by Mr. Lafferty Maths Department

www. mathsrevision. com S 4 General Simultaneous Equations Straight Lines Now try Ex 5 A Ch 7 (page 89 ) 2/23/2021 Created by Mr. Lafferty Maths Department

Starter Questions www. mathsrevision. com S 4 General 2/23/2021 Created by Mr. Lafferty Maths Department

Simultaneous Equations www. mathsrevision. com S 4 General Straight Lines Learning Intention 1. To solve harder simultaneous equations of 2 variables. 2/23/2021 Success Criteria 1. Apply the process for solving simultaneous equations to harder examples. Created by Mr. Lafferty Maths Department

www. mathsrevision. com S 4 General Simultaneous Equations Straight Lines Example 1 Solve the equations 2 x + y = 9 x - 3 y = 1 by elimination 2/23/2021 Created by Mr. Lafferty Maths Department

www. mathsrevision. com S 4 General Simultaneous Equations Straight Lines Step 1: Label the equations 2 x + y = 9 (A) x -3 y = 1 (B) Step 2: Decide what you want to eliminate Eliminate y by : 2 x + y = 9 (A) x 3 x -3 y = 1 (B) x 1 2/23/2021 Adding 6 x + 3 y = 27 (C) x - 3 y = 1 (D) 7 x = 28 ÷ 7 = 4 Created by Mr. Lafferty Maths Department

S 4 General Simultaneous Equations Straight Lines www. mathsrevision. com Step 3: Sub into one of the equations to get other variable Substitute x = 4 in equation (A) 2 x 4 + y = 9 – 8 y = 1 Step 4: The solution is x = 4 y = 1 Check answers by substituting into both equations 2 x + y = 9 x -3 y = 1 2/23/2021 ( 8 + 1 = 9) ( 4 - 3 = 1) Created by Mr. Lafferty Maths Department

www. mathsrevision. com S 4 General Simultaneous Equations Straight Lines Example 2 Solve the equations 3 x + 2 y = 13 2 x + y = 8 by elimination 2/23/2021 Created by Mr. Lafferty Maths Department

www. mathsrevision. com S 4 General Simultaneous Equations Straight Lines Step 1: Label the equations 3 x + 2 y = 13 (A) 2 x + y = 8 (B) Step 2: Decide what you want to eliminate Subtract Eliminate y by : 3 x + 2 y = 13 (A) x 1 2 x + y = 8 (B) x 2 2/23/2021 3 x + 2 y = 13 (C) 4 x + 2 y = 16 (D) -x = -3 x = 3 Created by Mr. Lafferty Maths Department

S 4 General Simultaneous Equations Straight Lines www. mathsrevision. com Step 3: Sub into one of the equations to get other variable Substitute x = 3 in equation (B) 2 x 3 + y = 8 – 6 y = 2 Step 4: The solution is x = 3 y = 2 Check answers by substituting into both equations 3 x + 2 y = 13 2 x + y = 8 2/23/2021 ( 9 + 4 = 13) ( 6 + 2 = 8) Created by Mr. Lafferty Maths Department

www. mathsrevision. com S 4 General Simultaneous Equations Straight Lines Now try Ex 5 B Ch 7 (page 90 ) 2/23/2021 Created by Mr. Lafferty Maths Department