2x-3y=19; X+4y =-7 solve using inverse matrix?

1 Answer
Jul 25, 2018

#x=5 and y=-3#

Explanation:

Here,

#2x-3y=19to(1)# , #and #

#x+4y=-7to(2)#

Let us write in the matrix equation form :

#((2,-3),(1,4))((x),(y))=((19),(-7))#

We take ,

#A=((2,-3),(1,4))# , #X=((x),(y))# ,#and B=((19),(-7))#

#:.AX=B#

Now, #detA=|(2,-3),(1,4)|=8-(-3)=11 !=0#

#:. "We can say that , " A^-1 " exists"#

Now ,#adjA=((4,3),(-1,2))#

#:.A^-1=1/(detA)*adjA#

#:.A^-1=1/11((4,3),(-1,2))#

We have,

#AX=B=>X=A^-1B#

#=>X=1/11((4,3),(-1,2))((19),(-7))#

Using Product of two matrices :

#X=1/11((76-21),(-19-14))#

#=>X=1/11((55),(-33))#

#=>((x),(y))=((5),(-3))#

#=>x=5 and y=-3#