State the system of inequalities whose solution is represented by the following graph.
First notice, that we’re supposed to state inequalities, that’s like greater than, less than, and so on. And it says “whose solution is represented by the following graph”, so this is the answer where these inequalities overlap. So a solution to inequalities is where the graphs overlap. So here we can see that in this shaded region.
So if we were to take two lines and then shade above or below them, how would they end up here? So this is the 𝑥-axis, and that’s where 𝑦 equals zero; so that’s the line. Now, to make it an inequality, we would want to shade above that line. So instead of 𝑦 equals zero, if we go above 𝑦 equals zero, that’s greater. So one, two, three, four, five, six, and so on for 𝑦. So that would be 𝑦 is greater than or equal to zero because we’re still included at zero. So that takes care of the going up portion.
Now since we don’t want that top left-hand corner, that’s actually called quadrant number two, we need to somehow cut that off. Well, with the line 𝑥 equals zero, it’s actually on the 𝑦-axis. So since we wanna take away that top left-hand quadrant, quadrant number two, and we just want the top right-hand corner, we wanna shade everything to the right of that line. So everything to the right of that line, 𝑥 will be increasing. So we need to change it from 𝑥 equals zero to 𝑥 is greater than or equal to zero.
So where these equations or inequalities overlap would be in the yellow, which is here. That’s where the 𝑦 is greater than or equal to zero and the 𝑥 is greater than or equal to zero overlaps. And that is the solution. So the system of inequalities would be these two inequalities together.
Therefore, our answer would be: 𝑥 is greater than or equal to zero, and then 𝑦 is greater than or equal to zero.