00:01
In order to solve this system of non -linear equations, i'm going to use substitution.
00:06
I'm going to choose to take our second equation and solve it for x.
00:11
That gives me x equaling 12 divided by y.
00:14
Now let's take that value of x and substitute it back into our first equation.
00:19
3 times x squared minus y squared equals 11.
00:26
Okay, getting rid of my parentheses, i have 432 over 1.
00:31
Y squared minus y squared equals 11.
00:36
I am going to multiply both sides of this equation by y squared, and i'm going to move everything to the right -hand side of my equal sign, so i can set it equal to zero.
00:47
Well, my first term will be 432, and moving it to the other side of my equation, will make that negative.
00:54
I will have y to the fourth, and 11 y squared.
00:59
This is a factorable equation.
01:03
I end up with y squared minus 16 or y squared plus 27.
01:10
And setting each of those factors equal to zero gives me these two values for y squared.
01:16
So what's the value of why? well, y squared equals 16 gives me two possibilities, either y equals four or y equals negative four.
01:27
Likewise, when y squared equals negative 27, that's two possibilities as well.
01:32
It's either going to be 3 square root of 3i or negative 3 square root of 3i.
01:40
4 possibilities for y.
01:43
Let's go back to our equation that i just marked in red, plug that value for y in and see what x comes out.
01:51
Well, the first two, the math is quite simple.
01:56
First one, x equals 3.
01:59
And if y is negative 4, x is negative 3.
02:06
So those are two options.
02:09
Now let's look at the others.
02:12
In this case, x is going to be 12 divided by y.
02:16
And i'd like to have a rationalized denominator.
02:19
So i'm going to multiply the top and the bottom by square root of three times i.
02:26
On the top, i will have 12 square root of 3.
02:30
In my denominator, the i squared is a negative, so i will have negative 9.
02:35
And that can simplify...