Explanation for Question 8 From the Math (Calc) Section on the 2019 October Sat
Now number eight, we're given a graph of a parabola and a line, 2 and it tells us that a systems of equations, 3 right? So that means that there's two equations here. 4 One of the equations is the parabola and the other equation is the life. 5 Um, and these equations are graphed in this system. 6 How many solutions does the system have? 7 So if you've seen a systems of equations, 8 you might know how to solve for X and Y, 9 but what we're really doing there is solving for the solutions and the solutions 10 are always where your two graphs or rather your two lines in 11 this case, one of them is a parabola intersect. 12 So when we, when we count solutions, 13 we're really counting intersection points. 14 We see an intersection right here and right here, 15 which means that there's really going to be two solutions. 16 And that's what's happening when also when both of our, 17 um, equations are lines in a systems of equation, 18 right? They'll intersect at one point, 19 but because one of our, um, one of our equations is a parabola. 20 In this case, we actually get two solutions, 21 which is shown as two intersection points. 22 And so the main takeaway from this problem is that going forward, 23 when you saw the systems of equations, know that the number of solutions that 24 you've solved for is also the number of times that your two equations will 25 intersect.