Simultaneous Equations
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Simultaneously means doing two this at the same time and Simultaneous Equations means doing two equations at the same time.
To start off with the right idea of simultaneous equation let's start out with an easy peasy problem
I went to a local store and brought three cans of coke and 4 packs of oreos which cost me £4.20.
Another day i brought two cans of coke and two packs oreos which cost me £2.60
how much does one can of coke cost?
c=cans o=oreos
first find the equation from the situation:
3c+4o= £4.20 - a
2c+2o=£2.60 - b
next substitute equation b into equation a as it is easier to work out
so we get 3 pounds +4c+4.20 pounds
next take three away from each side of the equation
3 pounds +4c= £4.20
-3 pounds -3pounds
now the equation looks like this:4c=1.20
but that ain't the answer yet
we still haven't found out how much one coke can costs so we divide 1.20 pounds by four
1.20 divided by 4 =30p
so one coke can costs 30p
we can check the answer by applying this knowledge into the problem
let's wrk this equation for a better way of understanding
firstly label each equation 1 and 2 so it is a little more visual
Equation 1: 2x + y = 7
Equation 2: 3x - y = 8
we must then add the two equation together to eliminate the y's
we do this because we can then find out the value of x and put that knowledge into the equation to find out y
2x + y = 7
3x - y = 8
------------
5x =15
x = 3
To start off with the right idea of simultaneous equation let's start out with an easy peasy problem
I went to a local store and brought three cans of coke and 4 packs of oreos which cost me £4.20.
Another day i brought two cans of coke and two packs oreos which cost me £2.60
how much does one can of coke cost?
c=cans o=oreos
first find the equation from the situation:
3c+4o= £4.20 - a
2c+2o=£2.60 - b
next substitute equation b into equation a as it is easier to work out
so we get 3 pounds +4c+4.20 pounds
next take three away from each side of the equation
3 pounds +4c= £4.20
-3 pounds -3pounds
now the equation looks like this:4c=1.20
but that ain't the answer yet
we still haven't found out how much one coke can costs so we divide 1.20 pounds by four
1.20 divided by 4 =30p
so one coke can costs 30p
we can check the answer by applying this knowledge into the problem
let's wrk this equation for a better way of understanding
firstly label each equation 1 and 2 so it is a little more visual
Equation 1: 2x + y = 7
Equation 2: 3x - y = 8
we must then add the two equation together to eliminate the y's
we do this because we can then find out the value of x and put that knowledge into the equation to find out y
2x + y = 7
3x - y = 8
------------
5x =15
x = 3
- Now you can put x = 3 in either of the equations.
- Substitute x = 3 into the equation 1 2x + y = 7
- 6(3x2) + y = 7
- subtract 6 from 7 to find out y
- y = 1