How do you solve #- x+y=6# and #-2x+y=7# using matrices?

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How do you solve #- x+y=6# and #-2x+y=7# using matrices?

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Answer 1 · 2016-02-09T18:11:33

#x=-1, y=5#

Explanation:

As the equations are already in the form #Ax+By=C#, writing all the coefficients of each equation to form each row of the matrix as below
#M=##[(-1,1,|,6),(-2,1,|,7)]#
Now by row operations change #2xx2# matrix on the left side to identity matrix.

#M=##[(1,0,|,-1),(-2,1,|,7)]#
Changed row 1 By subtracting row 2 from row 1

#M=##[(1,0,|,-1),(0,1,|,5)]#
Changed row 2 By adding 2 #xx#row 1 to row 2

From right column we obtain the solution as

#x=-1, y=5#

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How do you solve #- x+y=6# and #-2x+y=7# using matrices?

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