Explanation for Question 11 From the Math (Calc) Section on the 2019 October Sat
Now number 11, we're told that in an X, 2 Y plane, there's a graph of Y equals X plus three, 3 and it intersects the graph of Y equals two X minus six. 4 And we need to know what is the value of a, the X coordinate 5 of where they intersect. And so there was a question very similar to this 6 earlier in the exam. And what's important to know is that where two graphs 7 intersect is what we would call the solution solution. 8 So the systems of equations. So really what we need to do here is 9 take a systems of equations, plug it in and see what we can get 10 as our value of X for the solution. And in this case, 11 our system is going to be these two equations and 12 probably the best way to go about this is going to be to, 13 um, to use substitution as your way to solve the systems of equations, 14 because this equation has already solved for Y so I can take the X 15 minus the X plus three and plug it in for Y and my second 16 equation. 17 And I can rewrite it where instead of writing, Y I write X, 18 plus three is equal to the two X minus six, 19 and now I can easily solve for the X value, 20 which is what I want, because I also want a, 21 and the X value is a, and so what I can do is I 22 can start by getting all my exes to one side of the equation, 23 and I'll do that by subtracting X from both sides, 24 right? I get now that these exits cancel and I have three is equal 25 to X minus six. Now I need all my normal numbers. 26 So the other side of the equation can get that by adding six to 27 both sides. So three plus six that's nine is equal to X and these 28 cancel. So nine is equal to X and our X coordinate is our a 29 value, which means that a must be nine. 30 And our best answer is going to be C.