How do you solve #x - 2y = 5# and #2x - 3y = 10# using matrices?

1 Answer
Alan P.
Apr 5, 2016

Given
#color(white)("XXX") x-2y=5#
#color(white)("XXX") 2x-3y=10#

Re-writing as augmented matrix:
#color(white)("XXX") [(1,-2,5),(2,-3,10)]color(white)("XXX"){:([1]),([2]):} #

Subtracting #2# times the first row from the second row:
#color(white)("XXX") [(1,-2,5),(0,1,0)]color(white)("XXX"){:([1]),([3]=[2]-2xx[1]):} #

Adding #2# times row [3] to the first row:
#color(white)("XXX") [(1,0,5),(0,1,0)]color(white)("XXX"){:([4]),([3]=[1]+2xx[3]):} #

Re-writing with variables:
#color(white)("XXX")x=5#
#color(white)("XXX")y=0#

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