How to solve linear equations

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