Find the point of intersection of the pair of straight lines represented by the equation `6x^2+5x y-21 y^2+13 x+38 y-5=0.`

Answer

`(-32//23.17//32)`

Explanation

Let `phi(x,y)=6x^(2)+5xy-21y^(2)+13x+38y-5=0`. Differentiating with respect to x treating y as constant , we get
`(dphi)/(dx)=12x+5y+13`
Differentiating with respect to y treating x as constant , we get
`(dphi)/(dy)=5x-42y+38`
Solving equations `12x+5y+13=0and5x-42+38=0` we get
`x=-(32)/(23)andy=(17)/(23)`
Therefore , the point of intersection is `(-32//23,17//32)`.