How do you solve #3x - y = 8# and #-2x + y = 4# using matrices?

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Answer 1 · 2016-11-10T17:44:45

Please see the explanation.

Write #3x - y = 8# as the first row in an augmented matrix:

#[ (3, -1, |, 8) ]#

Write #-2x + y = 4# as the second row:

#[ (3, -1, |, 8), (-2, 1,|, 4) ]#

Add row 2 to row 1:

#[ (1, 0, |, 12), (-2, 1,|, 4) ]#

Multiply row 1 by 2 and add to row 2:

#[ (1, 0, |, 12), (0, 1,|, 28) ]#

The above augmented identity matrix translates into:

#x = 12 and y = 28#

check by substituting into the given equations:

#3(12) - 28 = 8#
#-2(12) + 28 = 4#

#8 = 8#
#4 = 4#

This checks