Explanation for Question 17 From the Math (Calc) Section on the 2020 October Sat
So question 17 asks us to solve for the value of X using 2 the systems of equations. As we can see here, 3 the bottom equation is already solved for Y. 4 So it would be very convenient to take that bottom part here, 5 plug it in for Y and then see what we can do from there. 6 So instead of writing why, when I rewrite this equation, 7 I'm going to write X minus seven is equal to X plus three times 8 X minus seven. And so now the next thing that I can do is 9 actually foil out this here so that I can 10 make sure that I've factored everything out. 11 Um, it's going to be better to get the full version and foil this 12 out and then factor from there. Because if you don't factor, 13 it's possible that you only get one solution when there's actually two answers to 14 the equation. 15 So best case scenario is just the factor or foil this out here get 16 X minus seven is X squared, minus seven X plus 17 three X minus 21. We can combine like terms here, 18 right? Cause these are both both X terms. 19 We get X squared minus four X minus 21. 20 And now we can take what's on the left side of the equation and 21 move it over to the right. It's like a subtract X from both sides. 22 I can add seven to both sides that way these guys cancel and I'm 23 left with zero over here and they get X squared minus five X not 24 plus minus 14. Now from here, 25 I can factor to solve for X. 26 Now I want two numbers that multiply to give me negative 14. 27 So maybe negative two and seven, 28 or we can d...