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#.