Solve system of linear equations, using matrix method, `2. x" "" "y" "=" "2` `3x" "+" "4y" "=" "3`

Explanation

Given system of equations,
2x-y=-2
3x+4y=3
`rArr" "[{:(2,-1),(3,4):}][{:(x),(y):}]=[{:(-2),(3):}]rArrAX=B`
`A=[{:(2,-1),(3,4):}]`
`rArr" "|A|=[{:(2,-1),(3,4):}]=8-(-3)=11ne0`
`therefore` A is iinvertible.
`"Now, "A_(11)=4, A_(12)=3, A_(21)=1, A_(22)=2`
`therefore" adj A ="[{:(4,-3),(1,2):}]=[{:(4,-3),(-3,2):}]`
`"and "A^(-1)=1/|A|"adj A=1/11[{:(4,1),(-3,2):}]`
From equation (1), A X= B
`[{:(x),(y):}]=1/11[{:(4,1),(-3,2):}][{:(-2),(3):}]=1/11[{:(-8,+3),(6,+6):}]=[{:(-5/11),(12/11):}]`
`therefore " "x=-5/11" and " y=12/11`