SOLUTION: Which is the best description of a system of linear inequalities for which there are no solution?
A)The lines are parallel
B)One inequality is the exact opposite of the other
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-> SOLUTION: Which is the best description of a system of linear inequalities for which there are no solution?
A)The lines are parallel
B)One inequality is the exact opposite of the other
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Question 291547: Which is the best description of a system of linear inequalities for which there are no solution?
A)The lines are parallel
B)One inequality is the exact opposite of the other
C)the lines do not intersect at a point in space
D)the lines are parallel and the shaded regions are opposite
E) cannot be described, all systems of linear inequalities have solutions Answer by Theo(13342) (Show Source):
OK if the equations were equality equations. NOT OK if the equations are inequality equations.
Selection B.
OK if the inequality is greater than and less than. NOT OK if the equations are greater than or equal and less than or equal.
Selection C.
OK if it's an equality equation. NOT OK if the equations are inequality equations.
Selection D.
This would work for all inequality equations.
Selection E.
This is clearly wrong. There are inequality equations where there is no solution.
Looks like Selection D is the best choice.
It says:
the lines are parallel and the shaded regions are opposite.
When this happens, There is a region between the lines that separates the equations regardless of the inequalities.
A graph of such an inequality would be something like:
y <= x + 3
y >= x + 5
the region of the equation y <= x + 3 has values on or below the line that satisfy that equation.
The region of the equation y >= x + 5 has values on or above the line that satisfy that equation.
None of the values that satisfy either equation will ever be common because there is a zone between the parallel lines that will always be empty and never crossed.
A graph of these 2 equations is shown below
For the equation of y >= x + 5, you would shade the area above the top line.
For the equation of y <= x + 3, you would shade the area below the bottom line.
