00:01
Since there's so much to do, i'm just going to jump right into the substitution with the very first one where i need to replace y in the top equation with negative 3x.
00:13
If you look at that top equation, y is being squared minus 3x squared equals 12.
00:22
At this point, just make sure that you know that negative 3, once you square, it's positive 9x squared minus 3x squared, which is a total of 6x squared, still equal.
00:33
To 12 that you could divide that six over.
00:36
So x squared will equal the square root.
00:39
Well, i still have to square root.
00:42
Just make sure that you give the positive and negative version of that answer, because now when you go back to that y equals negative 3x, and if you plug in the positive version, and for x here, then the ordered pair would be root 2, negative 3 root 2.
01:00
And then if you plug in the negative version in for x well negative times the negative is a positive 3 root 2.
01:07
So let's move on to number two and again i'm going to use substitution where you have the 3x squared minus 4x minus i'm going to take y out plus 4 equals 0 and i'm going to replace y with that negative 10x plus 1 because at this point make sure you distribute and combine like terms so i'm looking at 3x squared.
01:38
That would be a plus 6x.
01:40
A negative 1 plus 4 would be a 3 equal to 0.
01:45
And i can divide a 3 out of all of these.
01:49
So i'm just looking at x squared plus 2x plus 1 because that will make it easier for me to factor that factors of 1 be x plus 1, x plus 1.
02:01
And then you can quickly see that x would have to equal negative 1.
02:05
But remember you had that equation, and y equals negative 10 x plus 1.
02:10
So you have to plug in negative 1 right here.
02:13
So why negative 10 times negative 1 is a positive 10 plus 1, which is 11.
02:17
So your order pair would be negative 1, 11.
02:23
The next one, i actually have a plan past this one.
02:27
It looks very similar.
02:29
I would probably rewrite the adding 2y to the right side, x equals 2y plus 5.
02:36
So when you go to the next equation where you have an x being, squared plus y squared equals 50 you can replace that x with 2y plus 5 now make sure you foil that or whatever your teacher calls distributing that you'd have a 10 y plus 10 y is 20 y and then 5 times 5 is 25 yeah plus another y squared equals 50 and after you combine like terms all these are divisible by 5 so it would have been 5 y squared but when you divide by 5 would be just y squared and then 20 divided by 5 is 4 and if you subtract the 50 over and divide by 5 you get negative 5 so now factors of this one would be what's that negative or 5 minus 1 and for the sake of argument i'm just going to go ahead and write that the solutions are the opposite negative 5 and positive 1 and when you go back up here then and plug in negative 5 that x would equal negative 10 plus 5 would be negative 5.
03:51
So that's one ordered pair, negative 5, negative 5, and then plug in 1.
03:56
So x would equal 2 times 1 plus 5.
04:01
And so when x is 7, 2 times 1 plus 5, you get y is 1.
04:10
Kind of tired already.
04:12
The next one is not too bad.
04:13
I think what i would do is leave the first one alone, but i'm going to use elimination x squared plus y squared equal 7.
04:22
And i would negate everything in the second equation.
04:25
So negative x squared and then plus 2 y squared.
04:32
And i have to negate that 4 to be negative 4 because then i can add straight down.
04:39
And those x squared would cancel...