Are there more than one way to solve systems of equations by elimination?

1 Answer
Jan 14, 2015

There are more than one way to solve the system of equations

The most utilised methods are elimination and substitution methods. I prefer substitution than elimination.

Other methods like Cramer's rule and other matrix methods such as Gauss elimination, Gauss - Jacobi are available. These are pretty advanced and can solve any number of linear equations.

A comparison of substitution and elimination methods is given below.

Example

6x+4y=2---------->Eqn 1
x-2y=3---------->Eqn 2

Elimination method
Multiply Eqn 2 by '2' an add with Eqn 1.

6x+4y = 2
2x-4y = 6
______+
8x = 8
x =1

Substitute in one of the equations. Using Eqn 1 we have

6*1+4y = 2
4y = 2-6
y=-1

Hence the solution is x=1,y=-1

Substitution Method
From Eqn 2 we have

x=3+2y --> Eqn 3

Substitute in Eqn 1
6*(3+2y)+4y = 2
18+12y+4y=2
16y=2-18
16y = -16
y=-1
Use in eqn 3
x = 3+2.-1
x=1
So we get x=1,y=-1.