How can i use an inverse matrix to solve this equation? -x + y= 4, -2x + y = 0

1 Answer
Jul 22, 2017

Answer:

#x,y in { 4,8 }#

Explanation:

#-x+y=4, -2x+y=0#

Rewrite these equations using matrices

#((-1,1),(-2,1))((x),(y))=((4),(0))#

Let #A = ((-1,1),(-2,1))#

Then #A((x),(y))=((4),(0))#

And #((x),(y))=A^-1((4),(0))#

#det(A)=-1(1)-(-2)1=1 rArr A^-1=((1,-4),(2,-1))#

#((x),(y))=((1,-4),(2,-1))((4),(0))=((4),(8))#

#therefore x=4, y=8#

You may have noticed there's another way to do it. From the second equation, we get #y=2x#. Subbing this into the first equation allows us to solve for #x# and #y#