Simultaneous Equations (Solving with Algebra)

Simultaneous Equations (Solving with Algebra)Example (Substitution Method)Solve the Simultaneous Equation Below 3x - 2y = 0                                                                            [1]  2x + y = 7                                                                            [2] From [2] y = 7 – 2x Substituting in [1]                                            Substituting in [2] 3x – 2 (7 – 2x) = 0                                             2 x 2 + y = 7 3x – 14 + 4x = 0                                                  y = 3 7x = 14 X = 2 Therefore the solutions are x = 2 and y = 3

Example (Elimination Method)Solve the Simultaneous Equation Below2x + 3y = 5                                                                         [1]                          Substitute in [1] to find x 5x – 2y = -16                                                                       [2]                               2x + 3(3) = 5 [1 x 5]                                                                                                                    x = -2 10x x 15y = 25                                                                     [3] [2 x 2] 10x – 4y =  -32                                                                    [4] [3-4] 19y = 57 Y = 3 Therefore the solutions are x = -2 and y = 3

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