Solve the system of equations
x+2y=4
3x-4=5

Options

A. `x=1,y=2`
B. `x=1,y=3`
C. `x=2,y=1`
D. `x=2,y=3`

Answer

D

Explanation

Given equtios are
`x+2y=4`
`3x-y=5`
The equation can be written as `AX=B,` where `A=[{:(1,2),(3,-1):}],X=[{:(x),(y):}],B=[{:(4),(5):}]|A|=-1-6=-7ne0`, hence A is non-singular.
Given equation unique solution.
adj`A=[{:(-1,-2),(-3,1):}]`
`A^(-1)=[{:(-1,-2),(-3,1):}]=[{:(1/7,2/7),(3/7,-1/7):}]`
Now, `X=A^(-1)B=[{:(1/7,2/7),(3/7,-1/7):}][{:(4),(5):}]`
`[{:(x),(y):}]=[{:(4/7,+,10/7),(12/7,-,5/7):}]=[{:(14/7),(7/7):}]`
`[{:(x),(y):}]=[{:(2),(1):}]`
`rArr" "x=2, y=1`