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Study Hard Students by Tattooboy: 7:43pm On May 03, 2008 |
Simultaneous Equations Simultaneous equations are a set of equations which have more than one value which has to be found. At GCSE, it is unlikely that you will have more than two equations with 2 values (x and y) which need to be found. Example: A man buys 3 fish and 2 chips for £2.80 A woman buys 1 fish and 4 chips for £2.60 How much are the fish and how much are the chips? There are two methods of solving simultaneous equations. Use the method which you prefer. Method 1: elimination First form 2 equations. Let fish be f and chips be c. We know that: 3f + 2c = 280 (1) f + 4c = 260 (2) Doubling (1) gives: 6f + 4c = 560 (3) (3)-(2) is 5f = 300 \ f = 60 Therefore the price of fish is 60p Substitute this value into (1): 3(60) + 2c = 280 \ 2c = 100 c = 50 Therefore the price of chips is 50p Method 2: Substitution Rearrange one of the original equations to isolate a variable. Rearranging (2): f = 260 - 4c Substitute this into the other equation: 3(260 - 4c) + 2c = 280 \ 780 - 12c + 2c = 280 \ 10c = 500 \ c = 50 Substitute this into one of the original equations to get f = 60 . Harder simultaneous equations: To solve a pair of equations, one of which contains x², y² or xy, we need to use the method of substitution. Example: 2xy + y = 10 (1) x + y = 4 (2) Take the simpler equation and get y = , or x = , from (2), y = 4 - x (3) this can be substituted in the first equation. Since y = 4 - x, where there is a y in the first equation, it can be replaced by 4 - x . sub (3) in (1), 2x(4 - x) + (4 - x) = 10 \ 8x - 2x² + 4 - x - 10 = 0 \ 2x² - 7x + 6 = 0 \ (2x - 3)(x - 2) = 0 \ either 2x - 3 = 0 or x - 2 = 0 therefore x = 1.5 or 2 . Substitute these x values into one of the original equations. When x = 1.5, y = 2.5 when x = 2, y = 2 Simultaneous equation can also be solved by graphical methods by Tat |
Re: Study Hard Students by 4Him1(m): 11:43pm On May 03, 2008 |
put this on the algebra thread. |
Re: Study Hard Students by Tattooboy: 3:31pm On May 06, 2008 |
kindly do that |
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