Let's plot the given points (1,2), (4,-3), and (-2,8) to see where they lie.
We want points (1,2) and (4,-3) to be solutions of the system but not point (-2,8). Notice that both (1,2) and (4,-3) lie on the positive part of the x-axis while (-2,8) lies on the negative part of the x-axis. We can use this observation to write the first inequality of the system.
x≥ 0
Let's graph it and see if it works.
Since point (-2,8) does not belong to the solution set of the first inequality, it will never be a solution to the system. Let's now write the second inequality examining the y-coordinates of our two remaining points. They are 2 and -3. Therefore let's take, for example, all y-values less than or equal to 4.
y≤ 4
This gives us the following system.
x≥ 0 & (I) y≤ 4 & (II)
We can graph the system to make sure it all works like we were asked to.
Keep in mind that this is just one example of a possible solution.
