Explanation for Question 10 From the Math (No Calc) Section on the 2020 March Sat
So question number 10 tells us that B is a constant, 2 right? All that means is that no matter what happens, 3 B is always going to be the same number, 4 right? So the number that be is will never change. 5 And then it tells us the equation has infinitely many solutions. 6 What this means is that both sides of the equation, 7 the left and the right they're always going to be equal to each other, 8 no matter what the X value is. 9 And a good way to visualize this is by thinking of a graph. 10 If lines have infinitely many solutions, 11 that essentially means that they are the same line. 12 For example, this red line here and this green line here, 13 we can think that they're the same line because they cross through all the 14 same points. So the reason that's important is because if we have this equation 15 here and you're trying to solve for B, 16 you could first think, well, what do I put in for X? 17 And maybe this is where you got stumped, right? Um, 18 but because we have infinitely many solutions, 19 I could plug in any value for X and I would still get the 20 same for B, right? Because B is constant. 21 It never changes, no matter what X value you plug in. 22 And so whenever I get a chance to dish, just choose whatever X I 23 want to choose, I'll usually choose zero because that math is typically the easiest, 24 right? So I'm going to go ahead and plug in X for zero installed 25 for B. And if I do four times zero, 26 I know that's going to be zero. Over two is equal to two times 27 zero plus eight. So now we'll get rid of everything, 28 but zero, right? That's the four and the two. So I get B over 29 two is equal to eight. So to solve for B, 30 I just need to multiply both sides by two. 31 And that'll give me that B is equal to 16 and our correct answer 32 is going to be D okay.