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
b + 4f = $2.6
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
we have the third equation now
After this, we will eliminate the books...
3b + 12f = $7.8
3b + 2f = $2.8
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
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
b + 4f = $2.6
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
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 ^^
