Simultaneous Equations

Are the Equations ready to be added or subtracted?

Equations are ready to be added or subtracted if the numbers in front of the X or Y are the same.

E.g. 9y - 2x = 10

        4y - 2x = 5

In this example, you can see that both the x's are the same. They have the same signs too, this means you subtract them. When they have different signs (add, and minus) you add them

So lets work this example out.

9y-4y = 5y

10 - 5 = 5

now you divide 5y to find out what y equals, so Y = 5

So, what if the X's or Y's are different?

When they are different, there is an extra step you have to do. Lets take this as an example:

4x + 3y = 10

5x + y = 22

Right, so now you have to make them the same. so, how to you get them the same. as you can see, if you multiply the Y by 3, it can become the same. BUT REMEMBER YOU HAVE TO MULTIPLY EVERYTHING IN THE EQUATION BY THAT NUMBER.

4x + 3y = 10

15x + 3y = 66

5p + 5q = 35

2p +5q = 26

The signs are the same so you have to subracts the Q's to cancel them out, so you can find P

3p = 9 so P = 3

now you need to find what Q equals. for this you have to subsitute what you got for P into one of the equations (if you have a negative and a positive, always go for the positive) So, you now do

5 ( x 3) + 5q = 35

15 + 5q = 35

THIS IS NOW A SIMPLE EQUATION TO FIND WHAT Q IS. GIVE IT A GO! Make sure to write your answers clearly when you are done. P = 3 Q = 4

MORE EXAMPLES ON THE NEXT CARD!