Sometimes, you may need to rearrange the
equations before adding or subtracting
2x + y = 3 (1)
x - 3y = 7 (2)
If you simply add or subtract one of these
from the other, neither x nor y will be eliminated. Therefore you have to either
multiply the first equation by 3 or the second by 2 before you can proceed.
Method 2- substitution
1) Rearrange one equation to get either y
= _____ or x = _____
2) Substitute it onto the other equation
3) Solve the equation!
4) Use one of the original equations
to work out the other letter (x or y) that you do not already have
5) Check your answers in the other
equation
2x + y = 3
x - y = 1
---------------
1) y = 3 - 2x
2) x - (3 - 2x) = 1
3) x - 3 + 2x = 1
3x - 3 = 1
3x = 4
x = 4/3
x = 1^{1}/_{3}
4) 2(1^{1}/_{3}) + y = 3
2^{2}/_{3}
+ y = 3
y = 3 - 2^{2}/_{3}
y = ^{1}/_{3}
5) 1^{1}/_{3} - ^{1}/_{3
}= 1
1 = 1 ... so it worked!
Non-linear simultaneous equations
Use the method
of Substitution
x y = 2
(1)
x - y = 1
(2)
-----------------------------------------------------------------------------
Answer: x = y + 1 (2)
(y + 1) y = 2 [(1) with (2) substituted into it]
y^{2} + y = 2 [It is now a
normal quadratic]
y^{2} + y - 2 = 0
(y + 1)(y + 2) = 0
y = 1 or -2
Now find x
x = y + 1
x = 2 or -1