00:01
This problem says to solve the following system of inequalities graphically on the set of the axes below and state the coordinates of a point in the solution set.
00:10
So we'll graph both of these inequalities one at a time and the way we look for solutions of a system inequalities is by looking at where their shaded areas intersect, because that would be the area that has points that would be true for both inequalities, so that would be the system solution area, basically.
00:30
We'll start with y less than x minus 1, which has a y intercept of negative 1, and we have a slope of understood 1 in front of x.
00:37
We'd go up 1 over 1 a couple times.
00:40
We can also go down one left 1, and that gives us enough points to make our line.
00:44
But since we have a less than and not less than or equal to, we're going to connect these points with a dashed or dotted line.
00:55
And then when we look for the shaded area, the shaded area will take place wherever we would have y values less than our x minus one and this trick only works when you have y that comes first in comparison to your line so if my y values have to be less than x minus one from my y intercept negative one y less than would be down from there and that means that i'm going to shade everything on that side of the line so this first area of highlighted shaded area would be the solutions of our first line for our second line and we'll do this one in red, we would have to go to our y intercept again of negative 4, which would be here.
01:39
And then we would look at our slope again, and it turns out our slopes are the same, but that doesn't mean that we have no solution like with equations, because we're looking for not the intersection of the lines, but the intersections of their shaded areas.
01:52
So when we graph this line, going from negative 4 for our y intercept, and it looks like i accidentally have our y intercept at negative 5, not negative 4.
02:01
So it should be here.
02:02
When we go to graph, we use the same slope, up one over one, up one over one.
02:07
And again, we can go down one left one, two...