Simultaneous Equations
Solving simultaneous equations depends on making one of the letters disappear. To make the letter disappear, find a pair with the same number in front, then look at the signs in front of the numbers and then either add or subtract. To decide whether to add or subtract, do the opposite of the normal rule
|
|
|
|
OPPOSITE |
|
SAME |
+ + - - |
+ |
- |
|
DIFFERENT |
+ - - + |
- |
+ |
eg.1 (1)
(2)
’s match (both have 2 in front), both are
positive, the opposite of + + is -, so
take the equations away from each other
do this in your head
(1)
(2)
(1) (2):
so (
has disappeared)
(3)
Then substitute your result into either of the equations (1) or (2), whichever has the easiest numbers, and solve
(3) (1):
so, and
Test your answers by putting them into BOTH equations (1) and (2)
(1)
(correct)
(2)
(correct)
eg.2 (1)
(2)
these match, opposite of + - is + so add
(1) + (2) :
(3)
(
has disappeared)
(3) (1):
Check: (1)
(2)
Sometimes, neither of the two letters will match. In this case, either one or both equations need to be multiplied to get the numbers to match
eg.3 (1)
(2)
To make the ’s match, multiply (1) by 2
(3)
(2)
opposite
of + + is
(3) (2):
(4)
(4) (1):
Check: (1)
(2)
eg.4 (1)
(2)
(3)
(4)
(3) + (4):
(5)
(5) (2):
Check: (1)
(2)
NB: Notice the labeling system used. Instructions go in the left margins and labels go in the right margin