Explanation for Question 13 From the Math (No Calc) Section on the 2017 May Sat
Question 13 asks us for the point of intersection of these two equations 2 or these two lines, the point of intersection. 3 And when you have two lines is where X and Y have 4 the same value because that's when they touch on an X, 5 Y plane. When we are trying to find the X and Y 6 value of two lines, what we do assist them with equations. 7 When we're doing system of equations, we're really just solving to find out when 8 these lines intersect, which is when they have the same X and Y values. 9 So that's what we're going to do here. All we have to do to 10 find the point of intersection is system of equations. 11 Our first step in system of equations is getting one line or one equation 12 solve for one variable. And we already have that. 13 We have that in both of these. Our second step is to substitute that 14 into the second equation. 15 So we can do that by just plugging in five X plus one, 16 whenever we see Y in the second equation. 17 So when we do that, that would give us five X plus one equals 18 X squared, plus three X plus two, 19 but there's episodes to solve. So we're just going to solve for X. 20 And to do that, we want to get, um, 21 all the numbers on one side and all the common, 22 other terms on one side, we're going to first subtract 23 five X from both sides, and we get one equals X squared, 24 minus two X plus two. 25 And then we're going to drag the one from that side, you had zero 26 X squared minus two X plus one. 27 The reason why we want to have, 28 ...