How do you solve #2x + 7y = - 8# and #- 2x + 3y = - 12# using matrices?

1 Answer
Alan P.
Jun 23, 2017

#(x,y)=(3,-2)#
(see below for use of matrices)

Explanation:

Define the matrices:
#M_(xyc)=({: (x,y,=c), (2,7,-8), (-2,3,-12) :})#

#M_(xy)=({:(2,7),(-2,3):})color(white)("XX")M_(cy)=({:(-8,7),(-12,3):})color(white)("XX")M_(xc)=({:(2,-8),(-2,-12):})#

and their determinants:
#D_(xy)=|{:(2,7),(-2,3):}|=2xx3-(-2)xx7=20#

#D_(cy)=|{:(-8,7),(-12,3):}|=(-8)xx3-(-12)xx7=60#

#D_(xc)=|{:(2,-8),(-2,-12):}|=2xx(-12)-(-2)xx(-8)=-40#

By Cramer's Rule
#color(white)("XXX")x=(D_(cy))/(D_(xy))=60/20=3#
and
#color(white)("XXX")y=(D_(xc))/(C_(xy))=(-40)/20=-2#

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