[Video] Q27: In the xy-plane, the point (p, r) lies on the line with equation y = x + b, where b is a constant. the point with coordinates (2p, 5r) lies on the line with equation y =2x +b. if p not 0, what is the value of r/p ?

Explanation for Question 27 From the Math (Calc) Section on the Official Sat Practice Test 8

So question 27 has given us a little bit of information about two equations, 2 right? So we see two equations. And so that might initially clue us in 3 that we're trying to do something that's a little bit like systems of equations 4 with substitution or elimination. But another thing we know is that these are equations 5 for align and usually coordinates on a line are X comma, 6 Y but in this case, we're giving coordinates that are P comma are so 7 perhaps a good first step for this problem is to take these equations and 8 put the right variables in, cause we're not working with X and Y here, 9 we're actually working with PNR and that's our interest here for the answer we 10 want. PNR now says R come second. 11 That means ours. Like our Y coordinate. And since P comes first, 12 P is like our X coordinate. So we can rewrite this first equation here 13 to be in terms of R and P instead of X and Y. 14 And then we can do a similar thing in the second one, 15 where instead of just using PNR, we're going to use two P into art. 16 So our Y will be five R is equal to two times our 17 X, which is two P plus B, 18 oh, I wrote D here instead of B, let me change that. 19 Awesome. And so now what we're going to try to do is we're going 20 to try to get R and P into one equation. 21 That way we can combine them to get that ratio. 22 If we look at our two equations, we see that both of them have 23 a B in them. So something I can do is solve this topic equation 24 for B and then plug it in...