Simultaneous Equations. (Study thread)
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Simultaneous equations are a set of equations which have more than one value which has to be found.
Example:
A man buys 3 book and 2 file for $2.80
A woman buys 1 book and 4 file for $2.60
Find the amount each item...
There are two methods of solving simultaneous equations. Use the method which you prefer.
First method -->> Elimination.
First form 2 equations.
Let book be b and file be f.
We know that:
3b + 2f = $2.8 <--- (1)
b + 4f = $2.6 <--- (2)
Next, we need to find another Equation. We will name it (3).
(3) is need to eliminate an item so you will left with an item then you will be able to find the price of the item.
To form (3), we will need to borrow from either (1) or (2).
we will used (2) in this case.
3 x (2) = 3 x (b + 4f) = 3 x $2.6
3b + 12f = $7.8 <---(3)
we have the third equation now
After this, we will eliminate the books...
3b + 12f = $7.8 <---(3)
3b + 2f = $2.8 <--- (1)
10f = $5
f= $0.5
We have find The price for a file...
now we will find the price for a book.
3b and 2f is $2.8
3b + 2f = $2.8 <--- (1)
3b + 2(o.5) = $2.8
3b + $1 = $2.8
3b = $ 1.8
b = $1.8 / 3 = $0.6
So a book is $0.60 and a file is $0.50
Another method --->> Substitution. (recommended)
The same we need 2 equation.
3b + 2f = $2.8 <--- (1)
b + 4f = $2.6 <--- (2)
And also the same we need a third equation.
Rearrange one of the original equations to isolate a variable.
Rearranging (2)
b = $2.6 - 4f <--- (3)
Substitute (3) into (1).
3($2.6 - 4f) + 2f = $2.8
$7.8 -12f + 2f = $2.8
$5 = 10f
f= $0.5
Then the same... find b...
Substitution is recommended as you will seldom used elimination while doing harder question...
To solve a pair of equations, one of which contains x², y² or xy, we need to use the method of substitution.
Like this example.
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
You will get 2 answer for thing that involve ^2(square) or 3 answer if you have a ^3 (cube < A maths only> ).
Simultaneous Equations can also be in the form on line.
When 2 line intersect, you will need to used the equation of the 2 line to find what is X and Y.
Good luck studying ^^ -
Someone put up a topic on relativity please.
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simi lai de?Originally posted by stellazio:Someone put up a topic on relativity please. -
Google. Some Einstein theory.Originally posted by popikachu:simi lai de?
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Substitution is good when the numbers are small or there's no fraction involved after making x or y or whatever alphabet the subject.
For example:
2x + y = 0 - (1)
x + y = 1 - (2)
From (2),
x = 1 - y - (3)
Sub (3) into (1),
2(1 - y) + y = 0
2 - 2y + y = 0
2 - y = 0
-y = -2
y = 2
Sub y = 2 into (2),
x + 2 = 1
x = 1 - 2
= -1
This gives lesser chances of errors when working with fractions. Some people just anyhow cancel, which is wrong. Use elimination where possible. It's longer and tedious, but if you make careless mistakes, you will at least salvage some marks.
Anyhow canceling fractional algebra can give you zero. -
Some calculators actually can solve simultaneous eqns for u. dat adds as a bonus for you to check your answers
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Which partOriginally posted by stellazio:Someone put up a topic on relativity please.
Special or General -
some calculators cannot be used in o levelsOriginally posted by hiphop2009:Some calculators actually can solve simultaneous eqns for u. dat adds as a bonus for you to check your answers -
Doesn't really matter anyway. Most simple simultaneous equations are in Paper 1, those that require some reading and solving are in Paper 2.Originally posted by unclebutcher:some calculators cannot be used in o levels -
But it seems that those calculators are allowed ^^Originally posted by unclebutcher:some calculators cannot be used in o levels
Recommended by my teacher... -
The calculators allowed these days can surprise you.
Solutions to Simultaneous Equations are built the following 2 ideas:
1. You need as many equations as unknown variables.
i.e, If you have two unknown variables, you need 2 equations. If you have 3 unknown variables, you need 3 equations.
2. You simplify the problem to get rid of one of the variables, whether by the processes which today have been names substituition, or elimination.
Actually to me, its called elimination. period. expressing one variable as a form of the other, to eliminate one variable is called substitution. :p The point being that do not think of "Which method should I use ah?" as much as "How do I simplify this problem?" or "How do I get rid of X?"
If you understand these two principles, doing simultaneous equations even mentally should pose a lesser problem :p -
ah no....why cant he take note of how much each item cost in the book shop?
