Simultaneous equations

1
Simultaneous equations

• Yes, I know weve done this but you were a little
  ropey last week.

2
4 ways of solving them
3
1 Guessing the answers.

• Pros
• If you guess well, then easy to solve.

• Cons
• Hard to show your working.
• Only works for really simple ones.
• Can take a lot of time.

4
2 By adding/subtracting equations(traditional
method)

• Pros
• Works for all but the most complicated equations(
  A level).
• Will give exact answer.

• Cons
• Need to show all working and work carefully.
• May need to multiply equations first

5
3 Graphically

• Pros
• Will work every time
• Works for families of equations

• Cons
• Not always accurate
• Time consuming
• Long-winded, lots of room for mistakes to creep
  in.

6
4 Substitution

• Pros
• Can be quickest way
• Best way for complicated equations e.g.. powers

• Cons
• Not suitable for all equations
• More likely you are looking at A level paper.

7
Traditional approach
8
2x 2y 83x y 16

• Number equations
• 2x 2y 8
• 3x y 16
• Make ys the same by multiplying
• x 2 6x 2y 32

1
2
2
3
9
2x 2y 83x y 16

• 2x 2y 8 Same no. of ys in
• 3x y 16
• 6x 2y 32
• DIFFERENT signs so ADD
• 8x 40
• x 5

1
3
1
2
3
1
3
10
2x 2y 83x y 16

• 2x 2y 8
• 3x y 16
• Substitute x 5 in (easiest)
• 2 x 5 2y 8
• 10 2y 8
• 2y -2
• y -1

1
2
1
11
Almost there
12
2x 2y 83x y 16

• We have x 5 and y -1 so now we
• CHECK IT
• Check in because we havent used that yet
• (3 x 5) (-1) 15 - - 1
• 15 1
• 16

2
13
And finally..

• Dont forget to write your answers down clearly
• x 5 and y -1