Solve the system of equations`2/x+3/y+(10)/z=4`,`4/x-6/y+5/z=1`,`6/x+9/y-(20)/z=2`

Explanation

`"Let"1/x=p, 1/y=q, 1/z=r`
`therefore" Given system of equation"`
2p+3q+10r=4
4p-6q+5r = 1
6p+9q-20r=2
`[{:(2,3,10),(4,-6,5),(6,9,-20):}][{:(p),(q),(r):}]=[{:(4),(1),(2):}]rArrAX=B.....(i)`
`therefore" "A=[{:(2,3,10),(4,-6,5),(6,9,-20):}]`
=2(120-45)-3(-80-30)+10(36+36)
`=150+330+720=1200ne0`
`rArr" Ais invertible"`
`A_(11)=75, A_(12)=110, A_(13)=72`
`A_(21)=150, A_(22)=-100, A_(23)=-24`
` A_(31)=75, A_(32)=30, A_(33)=-24`
`therefore" adj A"=[{:(75,110,72),(150,-100,0),(75,30,-24):}]=[{:(75,150,75),(110,-110,30),(72,0,-24):}]`
`"From equation (1), AX=B" rArr X=A^(-1)B`
`rArr" "[{:(p),(q),(r):}]=1/1200[{:(75,150,75),(110,-100,30),(72,0,-24):}][{:(4),(1),(2):}]`
`=1/1200[{:(300,+150,+150),(440,-100,+60),(288,+0,-48):}][{:(1/2),(1/3),(1/5):}]`
`rArr" "p=1/2,q=1/3,r=1/5`
`rArr" "1/x=1/2,1/y=1/3,1/z=1/5`
`rArr" "x=2, y=3, z=5`