Explanation for Question 34 From the Math (Calc) Section on the 2018 March Sat
Question 34 says in the X, 2 Y plane, the lines that correspond to the system of equations above intersect 3 at the point a B what is the value of a over B? 4 So I'm going to start by taking this bottom equation here, 5 and I'm going to isolate Y so to do that, 6 I'm going to divide those sides by five. And that gives me, 7 Y is equal to three over five X. 8 Now that I know what Y is equal to, I can plug three over 9 five X into the Y value in this topic equation here. 10 So one over two times three, 11 over five X, just plugging that in for Y is equal to 19, 12 over 12 minus one, 13 over three X, 14 and now I can just solve for X. So this becomes three over 10 15 X is equal to 19, 16 over 12 minus one third X. 17 And then I can add one third X to both sides. 18 So three, 10 X plus one third X is equal 19 to 19 over 12. And then to add these two together, 20 I'm going to multiply this by three over three, 21 and this by 10 over 10. 22 And that gives me nine over 30 ax, 23 plus 10, over 30 X. 24 So nine plus 10, over 30 X, which is just equal to 19 25 over 30 X. 26 And we know that's equal to 19 over 12, 27 and then we can cross multiply and get 30 times 19 28 ax is equal to 19 times 12 and 29 divide both sides by 19 to get 30 X is equal 30 to 12. Finally, I can divide both sides by 30 and get X 31 is equal to 12 over 30, 32 which can be simplified to X is equal to two 33 over five. So now we know what our X value is, 34 and we need to plug that into our original equation to f...