If the points `A(3,\ 5)a n d\ B(1,\ 4)` lie on the graph of the line `a x+b y=7,` find the values of `a\ a n d\ b`

Explanation

Solution
If `'(3,5)'` lies on the line ax+by=7`.
Then
`'x=3,y=5, a(3)+b(5)=7`
`3a+5b=7`
`5b-7-3a`
`b=7/5-3a/5 ....(1)`
If `(1,4)` lies on the line `ax+by=7`
Then
`x=1,y=4, a(1)+b(4)=7`
`a+4b=7`
substitute the value of 'b' in the equation.
`a+4(7/5-3a/5)=7 a+(28/5-12a/5)=7`
`a-12a/5=7-28/5`
`5a/5-12a/5 = 35/5-28/5`
`-7a/5=7/5`
`-7a-7`
`a=-1`
substitute the value of 'a' in equation
...(1)
`b=7/53(-1)/5`
`b=7/5-(-3/5`
`b=7/5+3/5`

`b=10/5
b=2`
therefore,`a=-1,b=2`.