# 1 Press Ctrl-A ©G Dear2008 – Not to be sold/Free to use SimultaneousEquations Stage 6 - Year 12 Mathematic (Preliminary)

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1 Press Ctrl-A ©G Dear2008 – Not to be sold/Free to use SimultaneousEquations Stage 6 - Year 12 Mathematic (Preliminary)

2 Make ‘y’ the subject in 1. Substitute 1a into equation 2. 5x + 2 = 7 Equations Linear Simultaneous Equations Substitution Example 2x - y = -1 1. x + 2y = 7 2. y = 2x + 1 1a. 5x = 5 x = 1 x + 2(2x + 1) = 7 Sub x = 1 into 2. 1 + 2y = 7 2y = 6 y = 3 Solution (1, 3) y y

3 Equation 1. times 2 Add equation 2. and 1a. Equations 3 Linear Simultaneous Equations Elimination Example x = 1 2x - y =-1 1. x + 2y = 7 2. Sub x = 1 into 2. 1 + 2y = 7 2y = 6 y = 3 Solution (1, 3) 4x - 2y = -2 1a. 1.x2 5x = 5 1a+2

4 Equations Non-Linear Simultaneous Equations Substitution Example 3x + y = -2 1. y = x 2 2. Substitute equation 2 into equation 1. 3x + x 2 = -2 x 2 + 3x + 2 = 0 (x + 2)(x + 1) = 0 x = -2, x = -1 Sub x = -1 into eq. 2 Y = (-1) 2 = 1 Sub x = -2 into eq. 2 Y = (-2) 2 = 4 Solution (-1, 1) Solution (-2, 4)

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