00:00The absolute value of minus x plus 3 divided by 4 equals 3.
00:02The absolute value of 2 times y minus 1 equals x.
00:05The system states the sum of the y numbers that satisfy the requirement, folks.
00:09First, what is given to us in this system of equations?
00:12If minus x plus 3 in absolute value is 4 divided by 4 equals 3, how many roots can we get from this?
00:20Let's see how many x values we can get, guys.
00:22First of all, science 1 minus x plus 3 divided by 4 could be 3, right?
00:28There might be 3 people inside.
00:30Let's see what x is when it becomes 3.
00:32We said there was a hidden number 1 here, right?
00:34We can write it as 3 divided by 1.
00:36When we multiply by cross-multiplication, we get -x plus 3 equals 12.
00:42If I move x to the other side and this side, x equals minus 9.
00:47Okay, let's leave that aside for now.
00:48Now, secondly, the second of the first minus x plus 3 divided by 4 equals minus 3, so the outside, or the inside, is minus.
00:59It remains at 3.
00:59We can accept that it comes out as +3, right guys, in this system.
01:03Yes.
01:04Then, when this happens, it becomes the value of x in our equation.
01:07Again, assuming the denominator is 1, we perform the multiplication of "works, works, works".
01:11Minus x plus 3 equals minus 12.
01:13Alright.
01:14What happens if we move -x to this side and -12 to that side?
01:18Our x equals 15.
01:20So, it seems that the absolute value of our root x can take two values: one as -9 and one as 15.
01:25Alright.
01:26Now I'm coming to the second part, guys.
01:28He says, "And also in our system."
01:302 times minus 1 equals x in absolute terms.
01:34Could this x be minus 9, guys?
01:37It's connected through this system.
01:38This x and this x are the same.
01:39Could it be minus 9?
01:41No.
01:41It can't be -9, folks.
01:43We can't get rid of this root cause.
01:44From where?
01:44An absolute value expression could not produce a negative value expression.
01:47Absolute value would make it positive.
01:49Then the value we'll get here will simply be 15.
01:52Then if the absolute value is 2 times y minus 1 equals x, then that's also equal to...
01:57Its only value is 15, folks.
01:59Alright.
02:00If the absolute value is 2 times y minus 1 equals 15, then we get two values from this, in the same way again, friends.
02:06So, 2 times y minus 1 is minus 15.
02:10The inside is minus 15, or 2 times y minus 1 equals 15.
02:15What can we expect from this, guys?
02:16If we move -1 to the other side and solve these equations one by one, we get 2 times y equals -14.
02:22We find our Y to be minus 7 from here.
02:25Y becomes minus 7.
02:27Let's look at it from this perspective.
02:28We moved 2 times y minus 1 to the other side again, folks.
02:34It's 16 now.
02:34So what happened then?
02:36Our Y now equals 8.
02:39So, it seems our y can be 8 and our y can be -7.
02:42The question asked was to find the sum of the Y numbers.
02:45Y1 plus y2 equals 8 plus minus 7, which equals 1.
02:52So we're saying Denizli is the option.
02:542 times yi kills.
02:54In İlgel ***
02:54In Ilgel
02:54Hand-
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