How do you solve #x + 9y = 20# and #2x - 4y = 15# using matrices?

1 Answer
Bio
Feb 24, 2016

#x = 215/22#

#y = 25/22#

Explanation:

Writing the system in matrix form looks like this

#[(1,9),(2,-4)] [(x),(y)] = [(20),(15)]#

Now, the inverse of #[(1,9),(2,-4)]# happens to be #[(2/11,9/22),(1/11,-1/22)]#.

#[(1,9),(2,-4)]^{-1} = 1/(1xx(-4)-9xx2)*[(-4,-2),(-9,1)]^T#

#= [(2/11,9/22),(1/11,-1/22)]#

Multiply that to the left of both sides of the first equation, you will get identity matrix on the left side, and the answer on the right.

#[(2/11,9/22),(1/11,-1/22)][(1,9),(2,-4)] [(x),(y)] = [(2/11,9/22),(1/11,-1/22)][(20),(15)]#

#[(1,0),(0,1)] [(x),(y)] = [(215/22),(25/22)]#

#[(x),(y)] = [(215/22),(25/22)]#

You can check that

#(215/22) + 9(25/22) = 20#

#2(215/22) - 4(25/22) = 15#

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