There are 31 rabbits and 34 chickens in the field. There are some rabbits and chickens in a field Together they have 65 heads and 192 feet. How many rabbits?    How many chickens?   There are 31 rabbits and 34 chickens in the field. Extra for Experts: How many rabbits and chickens are in a field if the number of legs is three times the number of heads?

Simultaneous Equations by Substitution CW Date Simultaneous Equations by Substitution Lesson Objectives: Be able to solve simultaneous equations using the substitution method. Show all working out.

Changing the subject of a formula Sometimes we will need to rearrange a formula to find the value of a subject. For instance, we may know the area of a circle and need to find the radius. To do this, rearrange the formula to make the radius the subject. So area of a circle, A = π r2 A = π r2 [divide both sides by π] [Take the square root of both sides]

Changing the subject of a formula 1) Make x the subject: 5x – 2y = 9 + 4x 2) Make b the subject: 4b + 2c = a – b 3) Make y the subject: 4y = 9 – x + 3y 4) Make p the subject: p = a + 5q – 3 5) Make x the subject: 3ya2 = 5xc 4 minutes

What is the substitution method? What makes a set of simultaneous equations? Simultaneous equations are two equations with two unknowns. They are called simultaneous because they must both be solved at the same time. What is the substitution method? What do you think we might need to do?

Substitution method Solve the simultaneous equations: Equation 1: y = 2x – 10 Equation 2: x + y = 2 Equation 1 already has ‘y’ as the subject y = 2x - 10 Replace the ‘y’ in equation 2 by substituting it with 2x – 10 Equation 2 becomes: x + (2x – 10) = 2 3x -10 = 2 3x = 12 x = 4 Substituting x = 4 into Equation 2: 4 + y = 2 y = - 2

Step 3: Solve for eq.2 to find x Substitution method Solve the simultaneous equations: Equation 1: y - 2x = 1 Equation 2: 2y - 3x = 5 1 2 Step 1: Rearrange Equation 1, make ‘y’ the subject y = 1 + 2x Step 2: Replace the ‘y’ in equation 2 by substituting it with 1 + 2x (sub eq. 1 into eq. 2) Equation 2 becomes: 2(1 + 2x) - 3x = 5 Step 3: Solve for eq.2 to find x 2 + 4x - 3x = 5 2 + x = 5 x = 3 Step 4: Substituting x = 3 into Equation 1: y - 6 = 1 y = 7

Step 3: Solve for eq.2 to find d Substitution method - Example Solve the simultaneous equations: Equation 1: 2d + e = -8 Equation 2: 6d – 2e = 46 1 2 Step 1: Rearrange Equation 1, make ‘e’ the subject e = -2d – 8 Step 2: Replace the ‘e’ in equation 2 by substituting it with -2d -8 (sub eq. 1 into eq. 2) Equation 2 becomes: 6d - 2(-2d -8) = 46 Step 3: Solve for eq.2 to find d 6d + 4d + 16 = 46 10d = 30 d = 3 Step 4: Substituting d = 3 into Equation 1: 2d + e = -8 y = -14

You have 15 minutes to do as many as you can You have 15 minutes to do as many as you can. Show all your steps and working out.