Friday, 15 November 2013

simultaneous equations

using subtraction.


2x + 3y = 13
2x +2y = 10


first label the equations so you don't mix them up.

2x + 3y =13 - - - - - (1)
2x + 2y = 10 - - - - - (2)

you can't solve the equations because they have a x and y in them so we to cancel one out.

we can see there is 2x in both equations and if you subtract 2x from 2x you get 0.

so we have cancelled x out but we have to do the same to the rest of the equations to make it equal.
 (1) - (2)

2x -2x = 0
3y -2y =y
13 -10 = 3

so our equation looks like this

0 + y = 3

so...

y=3

 but we still need to work out x

to do this we need to put our answer for y into an equation.

 i am going to put it into equation (2) but it doesn't matter which one you put it into

 2x + 2y =10
2x +6=10
2x=10-6
2x=4
x=4/2
x=2 


so our answer to the simultaneous equation is y=3  and x=2


now try these



3x+2y=11
4x+2y=12


 x+3y=11
 x+5y=15

  3x+2y=32
  2x+2y=26

answers at bottom


using addition


2x+2y=10
-2x=y = -4


first label the equations so you don't mix them up.


2x+2y=10 ------ (1)
-2x+y = -4 ---------(2)


you can't solve the equations because they have a x and y in them so we to cancel one out.

we can see there is 2x or -2x in both equations and if you add 2x to -2x you get 0.

 so we have cancelled x out but we have to do the same to the rest of the equations to make it equal.

(2)+(1)

2x+-2x=0
2y+y=3y
10+-4=6

 0+3y=6
     3y=6
       y=6/3
       y=2



 but we still need to work out x

to do this we need to put our answer for y into an equation.

 i am going to put it into equation (1) but it doesn't matter which one you put it into


2x + 2y =10
 2x+4=10
 2x=10-4
2x=6
x=6/2
x=3


so our answer to the simultaneous equation is y=2 and x=3



now try these


2x+3y=16
3x-3y=-6


y+3x=16
24y-3x=9


x+4y=18
-x+=-3

answers at bottom











subtraction answers
x=1,y=4
x=5,y=2
x=6,y=7

addition answers
 x=2,y=4
x=5,y=1
 x=6,y=3




 tried and tested on my mum