Check Worksheet 3 On Socrative: Put in your answers to the selected questions. Room Name: mrcosgrove

Questions 25 – 28 *Solve like a normal equation. Example: |x| + 3 = 10 |x| = 10 – 3 |x| = 7 So x can be either +7 or - 7

Important Dates Diagnostic Test (not included on PowerSchool) Tuesday September 2nd Quiz on Review Sheets 1-4 Thursday September 3rd

Simultaneous Equations LO: To be able to solve Simultaneous Equations by adding or subtracting. Also called ‘Systems of Linear Equations’ STARTER: Expand & Simplify: 1)3(x + 4) + 4(x + 7) 2)2(3y + 6) + 3(2y – 4) 3)6(2m – 10) – 4(5m + 3) 1)7x )12y 3)-8m -72

=80p =£1.30 Why do we need to use Simultaneous Equations? = 50p = 30p

Why do we need to use Simultaneous Equations? Bronze: Solve: 6x + y = 15 4x + y = 11 Silver: Solve: 4x + 3y = 27 2x + y = 17 Gold: Solve: 2x + 3y = 30 5x + 7y = 71 When we have 2 different unknown letters, we can solve the equations at the same time (simultaneously).

Solving Simultaneous Equations – Example 1 Bronze: Solve: 6x + 1y = 15 (1) 4x + 1y = 11 (2) SAME SIGN SUBTRACT Step 1: Eliminate the letter with the same co-efficient (by SUBTRACTING in this question)… 6x + 1y = 15 4x + 1y = x = 4 x = 2 We have 2 unknowns: x and y Step 2: To find y, we substitute x = 2 back into one of the original equations (equation 1) (6 x 2) + y = y = 15 (-12) y = 3

Solving Simultaneous Equations – Example 1 Bronze: Solve: 6x + 1y = 15 (1) 4x + 1y = 11 (2) SAME SIGN SUBTRACT Step 3: Check your answers using equation (2)… x= 2, y = 3 (4 x 2) + 3 = = = 11 We have 2 unknowns: x and y

Silver: Solve: 3x + 3y = 18 (1) 5x + y = -2 (2) When Co-Efficient’s are not the same… SAME SIGN SUBTRACT Step 2: Eliminate the letter with the same co-efficient (by SUBTRACTING in this question) (3) 15x + 3y = -6 (1) 3x + 3y = 18 – 12x = - 24 (÷ 12) x = -2 Step 1: When neither co-efficient’s are the same we multiply one or both equations to make them the same… Multiply equation (2) by x3 15x + 3y = -6 (3) We call this equation (3) We use the original equation 1 and new equation 3.

Silver: Solve: 3x + 3y = 18 (1) 5x + y = -2 (2) When Co-Efficient’s are not the same… Step 3: To find y, we substitute x = -2 back into one of the original equations (equation 1) (3 x -2) + 3y = y = 18 (+ 6) 3y = 24 (÷ 3) y = 8 Step 4: Check your answers using equation 2 x = -2, y = 8 (5 x -2) + 8 = = = -2

Gold:Solve: 2x + 3y = 30 (1) 5x + 7y = 71 (2) When Co-Efficient’s are not the same… (A Grade) SAME SIGN SUBTRACT Step 2: Eliminate the letter with the same co-efficient (by SUBTRACTING in this question) (4) 15x + 21y = 213 (3) 14x + 21y = 210 – x = 3 So x = 3 Step 1: When neither co-efficient’s are the same we may need to multiply both equations to make them the same… Multiply equation (1) by x7 14x + 21y = 210 (3) We call this equation (3) Multiply equation (2) by x3 15x + 21y = 213 (4) We call this equation (4) Now we solve using equation (3) & (4)

When Co-Efficient’s are not the same… (A Grade) Step 3: To find y, we substitute x = 3 back into one of the original equations (equation 1) (2 x 3) + 3y = y = 30 (- 6) 3y = 24 (÷ 3) y = 8 Step 4: Check your answers using equation 2 x = 3, y = 8 (5 x 3) + (7 x 8) = = = 71 Gold: Solve: 2x + 3y = 30 (1) 5x + 7y = 71 (2)

Plenary The sum of two numbers is 19 and their difference is 5. Find the value of each of the numbers.

Review Sheet 4 Questions 1-5 Question 6 as extension