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**Simultaneous Equations**

The ‘Bare Bones’

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Main Points Solve two (or more) equations at the same time (simultaneously) Only one set of numbers will satisfy (work in) both equations If you set out your working carefully you can collect most of the marks even if your answer is incorrect

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**Rough Guide to solving sim. Equations.**

Always number your equations - this makes it easier to show your working. Take your time - these will be worth a lot of marks. No short-cuts.

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The ‘Nuts and Bolts’ You must have either the same number of x’s or y’s. - if not you will need to multiply one or more equations. Find either x or y by adding or subtracting and then substitute that value into one of the equations to find the other value. Always check your answers in the ‘remaining equation’

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**Same Sign Subtract Solve 2x + y = 8 and 5x + y = 17 - 3x + 0 = 9 x = 3**

Substitute x = 3 in x 3 + y = 8 so y = 2 Check in (not used directly to find y) 5 x = 17 so x = 3 and y = 2 1 2 2 1 1 2

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**Different Signs Add Solve 3x + 2y = 8 x - 2y = 0 + 4x + 0 = 8 so x = 2**

Substitute x = 2 in to find y 3 x 2 + 2y = 8 so 2y = so y = 1 Check in x 1 = 0 So x = 2 and y = 1 1 2 1 2 1 2

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**Different amounts of x and y**

Solve x + 2y = 11 and 3x + y = 18 Need either same number of x’s or y’s so x3 This gives 3x + 6y = 33 (SSS) y = so y = 3 Sub y = 3 in x + 2x3 = 11 so x = 5 Check in x5 + 3 = 18 so x = 5 and y = 3 1 2 1 3 3 2 1 2

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Fin The End

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Goal: Solve a system of linear equations in two variables by the linear combination method.

Goal: Solve a system of linear equations in two variables by the linear combination method.

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