[Video] Q11: X = 2y + 5 y = (2x - 3)(x+9) how many ordered pairs (x, y) satisfy the system of equations shown above?

Explanation for Question 11 From the Math (No Calc) Section on the Official Sat Practice Test 4

Now in number 11, we're asked how many ordered pairs satisfy the system of 2 equations above. And so that's a little unusual, 3 right? Normally we're just asked, what is the X value? 4 What is the Y value? But in this case, 5 what we should notice is that the X on the top equation has an 6 exponent of one, which shows us the top equation is a line. 7 And then here we see, okay, if I foil these out, 8 I actually get two X squared plus 18 X minus three X. 9 So plus 15 X minus 27. 10 So the exponent on that bottom equation is a two, 11 which tells us it's a parabola. 12 And if we think about the different ways that a line in a parabola 13 can intersect with each other, 14 there can either be zero intersections. 15 Like in this case, right here, we could have one intersection as in right 16 here, or we could have two intersections. 17 And so what's really key to remember is that when we talk about, 18 uh, solutions to a system of equations, 19 so this is some background info. When we talk about systems of equations solutions 20 are really just intersection points. 21 And so essentially when we're worried about the number of solutions, 22 what we need to do here is use quadratic formula because whatever's 23 underneath this radical and the quadratic formula is able to tell you how many 24 solutions you have. So what I'm going to do is I'm going to take 25 this equation here. I'm going to solve it for Y the top equation, 26 and I'm going to plug it in to my bottom equation. 27 So I...