pair of straight lines

for finding the slope you simply have to find the slope of the lines

6y²-xy-x² = 0

you get (3y+x)(2y-x)

so we get the above eqtn is of the form

(3y+x+a)(2y-x+b)

now compare coefficients....

Can you complete therest?

factorize..

or solve for y in terms of x

the above expression is a quadratic in both x and y

so you can solve either for x or for y