00:01
So the first thing we're being asked to do is to graph and shade the solution set for the given system of inequalities.
00:05
So we're going to start with our first equation.
00:07
X squared plus y squared is less than eight.
00:10
Well, well, this looks like the equation for a circle centered at the origin, because that equation is x squared plus y squared equals r squared.
00:17
So in this particular case, we just need to know our r value.
00:20
So r squared would equal to 8.
00:22
So to solve for r, we would take the square root of both sides.
00:25
Well, the square root of 8 is approximately 2 .83.
00:30
So that means we'd have a circle who centers at the origin, and if we go to the right about 2 .83, up from it to the left, and down, we could represent our circle.
00:41
But know this is strictly less than 8.
00:43
So that would mean that our circle would actually be a dash line, or i should say, a dash circle.
00:49
So now we have to figure out if we would shade inside the circle or outside.
00:53
So what we can do is do a test point.
00:55
So because our origin is inside the circle, i'm going to plug in 0 -0.
00:58
So if you have 0 squared plus 0 squared, we want to know if it's less than 8.
01:03
Well, 0 plus 0 squared plus 0 is 0, which is in fact less than 8, which means that we would shade everything inside the circle.
01:11
So everything inside the circle would represent the shaded area.
01:15
Okay.
01:16
Now, what we want to do is graph the inequality, y is less than 8 equal to x.
01:21
Well, think about what that means if you thought of it as an equation.
01:24
That means y is equal to x.
01:26
So this is our linear equation that has a slope of 1.
01:29
So it starts at the origin, and then it increases by a slope of one.
01:33
So it'll look like this.
01:35
And again, i'm graphing as a solid line because it's less than or equal to...