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