How do you solve using gaussian elimination or gauss-jordan elimination, #x+2y=7# , #3x-2y=-3#?

1 Answer
Jun 21, 2017

Answer:

#x=1# and #y= 3#

Explanation:

Rewrite this system in matrix form
#|1 2]# #[x]# #= [7]#
#|3 -2] ##[y]# # [-3]#

Now we want to put this matrix in triangular form. This amounts to eliminating y for instance.

Adding both rows yields
[1 2] [x] = [7]
[4 0] [y] [4]

In this form, you see that triangular means one equation will have all zero matrix element except one. In our case the bottom equation reads

#4x= 4#
The equation right above will have two non-zero matrix elements. Using the solution from the bottom equation, you can plug this solution into the equation above to get
#x + 2y = 7 #
#1 + 2y = 7#
or #2y = 6#
That is #y = 3#

Check
#x+ 2y = 1 + 2*3= 7#
#3x - 2y = 3 - 6 = -3#

That method only becomes efficient when you have more than two variables.