The coordinates of the point of intersection of lines `ax+by=9` and `bx+ay=5` are `(3,-1)`. Find the values of `a` and `b`.

Explanation

`{:(ax+by=9….(1),bx+ay=5….(2)):}`
The coordinates of the point of intersection are `(3,-1)`.
Substitute `x=3` and `y=-1` in equations `(1)` and `(2)`.
`{:(3a-b=9….(3),3b-a=5….(4)):}`
Multiply equation `(3)` by `3`,
`9a-3b=27`……`(5)`
Add equations `(4)` and `(5)`,
`{:(3b-a=5" ...(4)"),(-3b+9a=27" ...(5)"),("- - -"),(bar(" "" "8a""="32)):}`
`[,( :.a=(32)/(8),a=4):}`
Substitute `a=4` in equation `(4)`.
`{:(3b-4=5, :.3b=5+4, :. 3b=9, :.b=(9)/(3), :.b=3):}`