Recall how we find intersection points - we just solve the two equations together. So really you're just trying to determine if ax^2 + b = cx^2 + d has any solutions, or equivalently, if (a - c)x^2 = d - b has any solutions, or perhaps most simply, if x^2 = (d-b)/(a-c) has any solutions. If the right side of this equation is zero or positive, we'll be able to find one or two values of x, respectively. If the right side is negative, there will be no solutions. So we can rephrase the question: is (d-b)/(a-c)

> 0?

Since we need to know about both the numerator and denominator of (d-b)/(a-c), neither statement is sufficient alone. Combining the statements, since c = -a, our fraction becomes (d-b)/(2a). From Statement 2, d-b is negative. Still, we don't know if a is positive or negative; if a is positive, the fraction is negative, and if a is negative, the fraction is positive. Insufficient.

Of course, if you recognize that these are equations of parabolas, you can use coordinate geometry principles to solve. S1 tells us that one parabola is rising, one falling. Statement 2 tells us that the first parabola has a higher vertex than the second. Still, we have two possibilities; if the first parabola is rising, and the second falling, they don't intersect. If the first parabola is falling and the second rising, they do. Insufficient.

All that said, the wording of the question is very bad - the equations in the question clearly do not define 'lines'; they define 'curves'.

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