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Parallel and intersective lines solve for the intersections

I'm stuck on this question, would appreciate any help trying to figure this out:

Q)Two parallel lines and are crossed by a third line. Determine the coefficients of the third line such that the x-coordinate of the intersection of the two lines and is twice as much as that of the intersection of the two lines and ; and the y-coordinate of the intersection of the two lines and is twice as much as that of the intersection of the two lines and .

Calculate the coordinates of the two intersections.

Attachment 21946

I would appreciate any help on this.

Re: Parallel and intersective lines solve for the intersections

Solving you'll obtain .

Solving you'll obtain .

Now, using we get a linear system. Find and .

Re: Parallel and intersective lines solve for the intersections