How do you solve #4x + 5y = -7 # and #3x - 6y = 24# using matrices?

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Answer 1 · 2017-03-09T06:54:38

The solution is #((x),(y))=((2),(-3))#

We rewrite the equatins in matrix form

#((4,5),(3,-6))((x),(y))=((-7),(24))#

Let #A=((4,5),(3,-6))#

We need the inverse of matrix #A#

First, we calculate the determinant of matrix #A#

#detA=|(4,5),(3,-6)|=-24-15=-39#

As, #detA!=0#, the matrix #A# is invertible

#A^-1=-1/39((-6,-5),(-3,4))#

#=((6/39,5/39),(3/39,-4/39))#

Therefore,

#((x),(y))=((6/39,5/39),(3/39,-4/39))((-7),(24))#

#=((-42/39+120/39),(-21/39-96/39))#

#=((78/39),(-117/39))#

#=((2),(-3))#