Quiz Question 4 of 4 for PrepSwift: Calculating Intersections

In the solution, it states that you use the discriminate to find the number of solutions. In an earlier video, the discriminant is shown to be used to find the number of times in which the equation intersects with the x-axis (positive = twice, 0 = once, and negative = none).

Why is the discriminant being used to find number of intersections between two equations in this case instead?

The problem is essentially a simultaneous pair of equations, and we used substitution to get rid of one of the equations (and variables).

What does the equation 5x^2 - 7x + 4 = 0 even mean? It represents the possible values of x for which the two equations intersect each other. Can you now see how the discriminant is being used?

Ok, so if I’m understanding you correctly, when you combine two equations through substitution method, you are essentially using the discriminate in the same way you would if you just used it with one equation on the xy coordinate plane to find how many times that one equation intersects the x-axis?

And when you combine those two equations using substitution method, you are getting rid of the y-variable just like you would on a single equation on the xy coordinate plane to find where it intersects with the x-axis?