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

Q)Two parallel lines $\displaystyle y = 2x + 2$ and $\displaystyle y = 2x - 2$ are crossed by a third line. Determine the coefficients of the third line $\displaystyle y = ax + b$ such that the x-coordinate of the intersection of the two lines $\displaystyle y = ax + b$ and $\displaystyle y = 2x - 2$ is twice as much as that of the intersection of the two lines $\displaystyle y = ax + b$ and $\displaystyle y = 2x + 2$; and the y-coordinate of the intersection of the two lines $\displaystyle y = ax + b$ and $\displaystyle y = 2x + 2$ is twice as much as that of the intersection of the two lines $\displaystyle y = ax + b$ and $\displaystyle y = 2x - 2$.

Calculate the coordinates of the two intersections.

I would appreciate any help on this.