Simultaneous Equations
The ‘Bare Bones’
Main Points
• Solve two (or more) equations at the same
time (simultaneously)
• Only one set of numbers will satisfy (work
in) both equations
• If you set out your working carefully you
can collect most of the marks even if your
answer is incorrect
Rough Guide to solving sim.
Equations.
• Always number your equations - this makes
it easier to show your working.
• Take your time - these will be worth a lot of
marks.
• No short-cuts.
The ‘Nuts and Bolts’
• You must have either the same number of
x’s or y’s. - if not you will need to multiply
one or more equations.
• Find either x or y by adding or subtracting
and then substitute that value into one of the
equations to find the other value.
• Always check your answers in the
‘remaining equation’
Same Sign Subtract
1
Solve
2x + y = 8
and 5x + y = 17 2
2 - 1
3x + 0 = 9
x=3
Substitute x = 3 in 1 2 x 3 + y = 8 so y = 2
Check in 2 (not used directly to find y)
5 x 3 + 2 = 17 so x = 3 and y = 2
Different Signs Add
Solve
3x + 2y = 8 1
x - 2y = 0 2
1 + 2 4x + 0 = 8
so x = 2
Substitute x = 2 in 1 to find y
3 x 2 + 2y = 8 so 2y = 2 so y = 1
Check in 2 2 - 2 x 1 = 0
So x = 2 and y = 1
Different amounts of x and y
Solve x + 2y = 11 1
and 3x + y = 18 2
Need either same number of x’s or y’s so 1 x3
This gives 3x + 6y = 33 3
(SSS) 3 - 2
0 + 5y = 15 so y = 3
Sub y = 3 in 1
x + 2x3 = 11 so x = 5
Check in 2
3x5 + 3 = 18 so x = 5 and y = 3
Fin
The End