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Q: Can the solution of a system of linear inequalities be the points on a line?

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the answer is true

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It depends on whether the inequalities are strict or not.

An inequality determines a region of space in which the solutions for that particular inequality. For a system of inequalities, these regions may overlap. The solution set is any point in the overlap. If the regions do not overlap then there is no solution to the system.

It is a system of linear equations which does not have a solution.

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the answer is true

yes it is possible for a system of two linear inequalities to have a single point as a solution.

When there is an ordered pair that satisfies both inequalities.

its true because they have all have the same linear pair It's actually false

When the lines never intersect, usually when they are parallel.

A system of linear inequalities

It represents the solution set.

A solution to a linear inequality in two variables is an ordered pair (x, y) that makes the inequality a true statement. The solution set is the set of all solutions to the inequality. The solution set to an inequality in two variables is typically a region in the xy-plane, which means that there are infinitely many solutions. Sometimes a solution set must satisfy two inequalities in a system of linear inequalities in two variables. If it does not satisfy both inequalities then it is not a solution.

Which system of inequalities has a solution set that is a line?

3

Systems of inequalities in n variables with create an n-dimensional shape in n-dimensional space which is called the feasible region. Any point inside this region will be a solution to the system of inequalities; any point outside it will not. If all the inequalities are linear then the shape will be a convex polyhedron in n-space. If any are non-linear inequalities then the solution-space will be a complicated shape. As with a system of equations, with continuous variables, there need not be any solution but there can be one or infinitely many.

Linear system

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