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What is the difference between greater than and less than or equal to?
What type of lines never intersect?
Use a test point to determine which region to shade.
How are the solutions to a system of linear inequalities determined?
No, because they are parallel.
No.
No, see solution.
Equation (I) | Equation (II) |
---|---|
y=3x+3 | y=3x−5 |
y=3(0)+3 | y=3(0)−5 |
y=3 | y=-5 |
Since the lines have the same slope and are not identical, we know that the lines are parallel and will never intersect.
Let's take another look at the graph from Part A.
We can see that the shaded regions do not overlap. Additionally, because the boundary lines are parallel, as we found in Part B, the shaded regions will remain an equal distance apart for as long as the lines continue. Therefore, they will never overlap.
The solution set of a system of linear inequalities can be interpreted as the intersection of shaded regions of graphs of all the inequalities in the system. Since the graphs do not, and will never, overlap, there are no solutions to this system.