Question

Question #2ed49

Answer 1

`alpha=1/2`
`beta=-1/3`
`gamma=1`

Explanation:

let `a=1/alpha` , `b=1/beta` , `c=1/gamma`

`=>`

`4a-b+c=12 => c=12+b-4a`
`2a+2b+3c=1`
`5a-2b+6c=22`

`=>`

`2a+2b+3*(12+b-4a)=1`
`5a-2b+6*(12+b-4a)=22`

`=>`

`2a+2b+36+3b-12a=1`
`5a-2b+72+6b-24a=22`

`=>`

`-10a+5b=-35`
`-19a+4b=-50`

`=>`

`-2a+b=-7 => b=-7+2a`
`-19a+4b=-50`

`=>`

`-19a+4*(-7+2a)=-50`

`=>`

`-19a-28+8a=-50`

`=>`

`-11a=-22 => a=2`

`=>`

`b=-7+2*(2)=-3`

`=>`

`c=12+(-3)-4*(2)=1`

`=>`

`2=1/alpha => alpha=1/2`
`-3=1/beta => beta=-1/3`
`1=1/gamma => gamma=1`

check:

`4/(1/2)-1/(-1/3)+1=8+3+1=12`

`2/(1/2)+2/(-1/3)+3/1=4-6+3=1`

`5/(1/2)-2/(-1/3)+6/1=10+6+6=22`