Question

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

Answer 1

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`.