
a.
Find a system of inequalities.
a.

Answer to Problem 46HP
Explanation of Solution
Given information:
The solution lies in the third quadrant.
Calculation:
Confining the first inequality to just quadrant
Again, confining the second inequality to just quadrant
Together, these inequalities define a space strictly contained in quadrant
Hence, the inequality of a solution that lies in the third quadrant is
b.
Find a system of inequalities.
b.

Answer to Problem 46HP
Explanation of Solution
Given information:
The solution that does not exist.
Calculation:
The inequality that defines a region lying above and along the line
The inequality that defines a region lying below and along the line
These lines are parallel with slope. One region lies above the upper line, while the second region lies below the lower line. So, these regions have no common points and also, no solution. So we get this region as,
Hence, the inequality of a solution that does not exist is
c.
Find a system of inequalities.
c.

Answer to Problem 46HP
Explanation of Solution
Given information:
The solution that lies only on a line.
Calculation:
The inequality that defines a region lying above and along the line
The inequality that defines a region lying below and along the line
The only points that these inequalities share are those along the line
Hence, the inequality of a solution that lies only on a line is
d.
Find a system of inequalities.
d.

Answer to Problem 46HP
Explanation of Solution
Given information:
The solution that lies on exactly one point.
Calculation:
The inequality that defines a region lying along and between the line
The inequality that defines a region lying below and along the
The only points that these inequalitieshave in common is the origin (this would not be true if strict inequalities were used). So, we get,
Hence, the inequality of a solution that lies on exactly one point is
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