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Here’s your shmoop du jour… The following graph represents the solution
set to which of the following systems of inequalities in two variables?
Here are the potential answers…
So… what is this question asking?
Ok sooo… what in the world is a solution set, first of all?
Well, it’s the set of all points that answers a given equation.
Like… if the inequalty was “x is greater than 0,” then the whole right side of a
graph would be shaded in like this…
But here we have complexities in the form of oddball equations which are all the same,
so we know the equations we're given in our answer solutions are the equations of the
symbols. From the graph, we can see that one line is
dotted, while the other is solid.
We know that a “less than” or “greater than” inequality without the “equals to”
signifies a dotted line…
…and that a “less than or equal to” and a “greater than or equal to” inequality
signifies a solid line.
So, because we have one of each in our graph, we know our answer solution has to have one
inequality with an equals sign and one without.
We can immediately eliminate A and D, since they aren’t following the rules.
Now we can look closer at the actual equations.
Not that close.
The dotted line has the equation y equals -x + 3, and in the graph, the shaded region
is above this line.
So we know the inequality must be “y is GREATER THAN negative x plus 3.”
Only B has this inequality, so D is S-O-L.
Looks like our answer is B.
As in, “Best Christmas ever.”