00:00x and y are distinct real numbers.
00:03Given that 2 times x squared minus 5 times x times y plus 3 times y squared equals 0,
00:08We are asked to find the ratio of 4 times x minus 5 times y divided by x minus y.
00:12Guys, what is this information I'm looking for?
00:142 times x squared minus 5 times x times y plus 3 times y squared equals 0.
00:21Can we factor this from here?
00:22Let's try separating.
00:23If I say 2x to x and then minus 3y to minus y, their product gives 3y squared.
00:31When I do cross-multiplication and add the results here, what do I get, friends?
00:35It gives the middle ground.
00:36So, we can write it like this, folks.
00:392x minus 3y multiplied by x minus y equals 0.
00:44In fact, when I bring it here, I see it as 2 times x minus 3y times x minus y equals 0, which is 1.
00:52Either 2x minus 3y equals 0, or the second one will be x minus y equals 0.
01:00Could Ex minus y be 0, guys?
01:02X and Y are said to be different from each other.
01:03If x minus y equals 0, then x equals y, right?
01:07When we move the minus y to the other side.
01:09That's why it's impossible, folks.
01:11And also, when we substitute this here, the denominator is 0, which makes it undefined.
01:15This won't let go, this is a hit.
01:17So, now that he's gone, this is what we're left with, folks.
01:19If 2 times x minus 3 times y equals 0, then 2x equals 3y.
01:25So, I'm saying that the proportionality constant should be equal to 6 times k, guys.
01:29What does our K stand for here?
01:32The real number is the difference, except for 0.
01:36Ok.
01:37Since this is excluding 0, when I substitute 2 times x = 6k, I can say x = 3k.
01:43And if I divide y by 3, which is y equals 2 times k, I can give both sides, right guys?
01:49I could have given 3k instead of x and 2k instead of y.
01:51Since he was asking about the ratio, it's highly likely that the 'k's will cancel each other out here.
01:56Let's take a look, guys.
01:57The question was 4 times x minus 5 times y divided by x minus y.
02:02Instead of multiplying 4 by x, I'm writing 3k.
02:05I'm writing -5 times 2k, and instead of y, I'm writing x minus y, which equals what?
02:123k minus 2k equals 4k, which is 3k = 12, and here it becomes 10k.
02:17How much does it take, guys?
02:18What is 12k minus 10k divided by, guys?
02:23K is equal to our answer, friends. We find the answer as 2k divided by k, which is 2.
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