SOLUTION: Can the graphs of two linear inequalities be drawn with the given intersection? It would be great if you would answer the question for all four intersections given. a. a point

Question 700985: Can the graphs of two linear inequalities be drawn with the given intersection? It would be great if you would answer the question for all four intersections given.
a. a point
 b. a line
 c. a region
 d. no intersection

Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Yes for all.

a. You need a pair of single variable inequalities in the same variable such that the intersection of the solution set is a single value. If you are restricted to two-variable inequalities, then the answer is No, the solution set cannot consist of a single point.

and

for example.

b. You need a pair of two-variable linear inequalities such that both boundary lines are included in the solution set of each and the intersection of the two solution sets is the boundry line.

and

for example.

d. (purposely out of order). You need a pair of two-variable linear inequalities such that the boundary lines are parallel lines and the intersection of the two solution sets is the empty set.