There are many methods to solve linear equations, such as:
1. Equating method: Let's take two simultaneous linear equations x+y=5 and x-y=1.
x+ y=5 can be written as x = 5-y.........(1)
In the same way,
x-y=1 or, x = 1+y.............(2)
Here, we equate the two equations and get the value of unknowns.
2. Substituting method: Again, take the equations x+y=5 and x-y=1.
x+y=5
or, x=5-y.........(1)
x-y=1............(2)
Substituting equation (1) in (2),
(5-y) - y=1
or, 5-2 y = 1
or, y = 2.
This is called substitution method.
3. Formula method: simultaneous linear equations can also be solved by formula.
If there are two equations: ax+by +c=0 and d x+e y+f=0 then the solution of such equation would be:
x = (bf - e c)/( a e - db), y = (a f-dc)/(db - a e).
For example,
2 x+ 3 y = 10 or, 2 x +3 y-10=0..................(1)
x+y=-44 or, x+y+44=0..................(2)
Comparing equation (1) and (2) with ax+by+c = 0 and dx+ey+f=0, a=2, b=3, c=-10, d =1, e=1, f=44.
Using formula,
x= -142 and y = 98.
4. Graphical method
5. Elimination method
6. Matrix method
