If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains ***.kastatic.org** and ***.kasandbox.org** are unblocked.

Main content

Current time:0:00Total duration:5:36

CCSS.Math:

graph the solution set for this system it's a system of inequalities we have Y is greater than X minus 8 and Y is less than 5 minus X so let's graph the solution set for each of these inequalities and then essentially where they overlap is the solution set for the system the set of numbers that's or the set of coordinates that satisfy both so let me draw a coordinate axes here so that is my x-axis and then I have my y-axis and that is my y-axis and now let me draw the boundary line the boundary for this first inequality so the boundary line is going to look like Y is equal to X minus 8 but it's not going to include it because it's only greater than X minus 8 but let's just graph X minus 8 so we're the y intercept here is negative 8 when x is 0 Y is going to be negative 8 so let's go negative 1 negative 2 3 4 5 6 7 8 so that is negative 8 so the point 0 negative 8 is on the line and then it has a slope of 1 this is a you don't see it right there but I could write it as 1 X so the slope here is going to be 1 I could just draw a line that goes straight up or you could even say that it'll intersect if Y is equal to 0 if Y we're equal to 0 X would be equal to 8 so 1 2 3 4 5 6 7 8 and so this is X is equal to 8 if it has a slope of 1 for every time you move to the right 1 you're going to move up 1 so the line is going to look something like this and actually let me draw it not drawn as a solid line if I did it as a solid line that would actually be this equation right here but we we're not going to include that line we care about the Y values that are greater than that line so what we want to do is do a dotted line to show that that's just the boundary that we're not including that we're not including that in our solution set let me do this in a new color so this would be this will be the color for that line or for that inequality I should say so that is the boundary line and this says y is greater than X minus 8 so you pick an X and then X minus 8 would get us on the boundary line and then Y is greater than that so it's all the Y value is above above the line for any given X so it'll be this it'll be this region above the line right over here and if that confuses you I mean in general I like to distinct oh great er then it's going to be above the line if it's less than it's going to be below a line but if you want to make sure you can just test on either side of this line so you could try the point zero zero which should be in our solution set and if you say zero is greater than zero minus eight or zero is greater than negative eight that works so this definitely should be part of the solutions and then you could try something out here like like ten comma zero and see that it doesn't work because you would have 10 minus 8 which would be 2 which and then you would have zero and zero is not greater than two so when you test something out here you also see that it won't work but in general I like to just say hey look this is the boundary line and we're greater than the boundary line for any given X now let's do this one over here let's do this one the boundary line for it is going to be y is equal to five minus x so the boundary line is y is equal to 5 minus x so once again if x is equal to zero Y is 5 so 1 2 3 4 5 and then it has a slope of negative 1 we could write this as Y is equal to negative 1 X plus 5 that's a little bit more traditional so once again y intercept at 5 it has a slope of negative 1 or another way to think about it when y is 0 when y is 0 X will be equal to 5 so 1 2 3 4 5 so every time we move to the right one we go down 1 so we have a negative 1 slope so it will look it will look like this and once again I want to do a dotted line I want to do a dotted line because we are so that is our dotted line and I'm doing a dotted line because it says y is less than 5 minus X if it was look if it was y is equal to 5 minus X I would have included the line if it was y is less than or equal to 5 minus X I also would have made this line solid but it's only less than so for any x value for any x value this is what 5 minus x 5 minus X will sit on that boundary line but we care about the Y values that are less than that so we want all everything that is everything that is ball hello the line and once again you can test on either side of the line zero zero should work for this second inequality right here zero is indeed less than five minus is zero zero is less than five and you could try something like zero ten and see that it doesn't work because if you had ten is less than five minus zero that doesn't work so it is everything below the line like that and like we said the solution set for this system the solution set for the system are all of the X's and Y's all of the coordinates that satisfy both of them so all the shaded in purple satisfies the second inequality all the shaded in green satisfies the first inequality so the stuff that satisfies both of them is their overlap so it's all of this region in blue hopefully this isn't making it too messy all of this region in blue where the two overlap below the magenta dotted line on the left-hand side and above the green magenta line that's only where they overlap so it's only this region only this region over here and you're not including the boundary lines