How do you solve #5x + 3y = -8# and #4x + 6y = 8# using matrices?

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Answer 1 · 2018-06-27T09:12:07

The solution is #((x),(y))=((-4),(4))#

The equation in matrix form is

#AX=B#

where

The matrix #A=((5,3),(4,6))#

#X=((x),(y))#

and

#B=((-8),(8))#

The solution is

#X=A^-1B#

The inverse of #A# is

#A^-1=1/|(5,3),(4,6)|((6,-3),(-4,5))#

#=1/18((6,-3),(-4,5))#

Therefore,

#X=1/18((6,-3),(-4,5))((-8),(8))#

#=1/18((-72),(72))#

#=((-4),(4))#

The solution is

#((x),(y))=((-4),(4))#