How do you solve using gaussian elimination or gauss-jordan elimination, #2x + 6y = 16#, #2x + 3y = -7#?

1 Answer
Jun 23, 2016

Answer:

#(x,y)=color(blue)(""(-15,23/3))#
(see below for gaus-jordan elimination)

Explanation:

Writing the given equations in augmented matrix form:

#((2,6,16),(2,3,-7))#

Pivot element: row:1, column:1
divide all entries in row 1 by 2 in order to reduce the pivot element to 1

#((1,3,8),(2,3,-7))#

subtract 2 times row 1 from row 2 to zero the non-pivot element in the pivot column

#((1,3,8),(0,-3,-23))#

Pivot element: row:2, column:2
divide all entries in row 2 by (-3) in order to reduce the pivot element to 1

#((1,3,8),(0,1,23/3))#

subtract 3 times row 2 from row 1 to zero the non-pivot element in the pivot column
(this is the step that converts it from gaussian elimination to gaus-jordan elimination)

#((1,0,-15),(0,1,23/3))#

Writing this in non-matrix form:
#color(white)("XXX")x=-15#
#color(white)("XXX")y=23/3#