Find the straight line passing through the point of intersection of `2x+3y+5=0,5x-2y-16=0` , and through the point `(-1,3)dot`

Explanation

The equation family of lines through the point of intersection of the given lines is
`2x+3y+5+lambda(5x-2y-16)=0 " "(1)`
If a member of the above family of lines passes through the point (-1,3), then
`2(-1)+3(3)+5+lambda(5(-1)-2(3)-16) = 0`
`"or " lambda = (4)/(9)`
Putting this value `lambda` in equation (1), we get the required equation of line as
9(2x+3y+5)+4(5x-2y-16)=0
`" or " 2x+y-1=0`