Maybe I'll circle that one, I could have circled that one.

Chance, the flip of the coin, doesn't get the choice of one direction or the other.

And so we have 2y times 2y minus 3, plus 5 times 2y minus 3.

They both have one 5 that's one 5, one 5.

So they both deserve at least a price to earnings of 10.

Now, what if I were to ask you, is there an x and y pair that satisfies both of these equations?

Or you could say if x is great well, you could go both ways in that.

They'll say 'No, you can't go that way.' They're gonna close up. They won't allow blood to go that way.

Sal Let's check our answer.

We have x squared on both sides of this, we subtract x squared from both sides of the equation.

If you have magnetic fields, you don't go anywhere.

Well, you look at it here, it's going to be this point.

The absolute value of negative 11 is 11, so we get 11 is equal to 11, so they BOTH work.

You'll probably notice some similarities but also some differences.

Do they both understand Japanese?

In total for this model there is 11 different words.

Somebody said we are super poor, and we are also super power.

You both have a pleasant day too.

We want the right side to just be x minus 1.

And I want to do that because I saw this b minus k out there so that looked interesting to get it on both terms right there.

And if we just look at this by inspection we see, well, they both share one, but that's nothing special.

So because this expression is negative and we want to get back to this expression, we want to get back to this x minus 1, we need to take the negative square root of both sides.

Also you could take use INT the INT function which will convert that string into an integer.

Let me do that.

So we have two mixed numbers here, and like when you're adding mixed numbers, you can do it two ways.

You can divide the numerator and the denominator by 9.

So these are just constants from an x point of view, so this is all going to be 0.

Now that seems a little bit nonsensical.

So that the value does not change.

So that would be 3x squared plus 1.

I'd like to say a few final words about supervised versus unsupervised learning.

Rational is not a subset of irrational, they are exclusive.

And the top two problems, this one right here both 1s are positive.

There's something to cancel out.

The first equation is x 2y 13, second equation is 3x y 11, Inorder for 1,7 for solution for the system it needs to satisfy both equations. x 1 and y 7, need to satisfy both equations to be a solution.

So this might look a little daunting at first.

There's no way that I can have remember there's an and here.

So if we factor out a 2x plus 5 from both of these so we're factoring out a 2x plus 5, you're left with an x and a plus 4.

Second we need to reproduce the steps required to reproduce the problem.

This isn't any kind of fancy factoring.

Both, actually.

Now, we aren't dealing with only the blue constraint or only the red constraint.

Anywhere where there is a 0 and 1, and a 0 and the other, it's going to be 0.

So one way to solve these systems of equations is to graph both lines, both equations, and then look at their intersection.

Five symmetries and then of course the zeroth symmetry where I just pick it up and leave it where it is.