In each of the fowllowing cases, find a and b
(i) `(2a+b,a-b)=(8,3)`
(ii) `((a)/(4),a-2b)=(0,6+b)`

Explanation

we have,(2a+b,a-b) =(8,3)
`rArr " " 2a+b=8and a-b=3`
[since, two ordered paris are equal, if their corresponding first and second alements are equal]
On substituting b=a-3 in 2a +b=8 , we get
`" " 2a+a-3=8rArr 3a-3=8`
`rArr" " 3a=11rArra=(11)/(3)`
Again, `" " ` Substituting `a=(11)/(3)` in b=a-3, we get
`b =(11)/(3)-3=(11-9)/(3)=(2)/(3)`
`:. a=(11)/(3) and b=(2)/(3)`
(ii) We have, `((a)/(4),a-2b)=(0,6+b)`
`rArr (a)/(4)=0rArra=0`
and a-2b=6+b
`rArr0-2b=6+b`
`rArr-3b=6`
`:. b=-2`
`:. a=0,b=-2`