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Q: A system of two linear inequalities has either no points or infinitely many points in its solution?

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None, one or infinitely many

yes

A linear inequality is all of one side of a plane. A quadratic inequality is either the inside of a parabola or the outside.

A system of linear equations can only have: no solution, one solution, or infinitely many solutions.

Infinitely many. The solution space is part of a plane.

Related questions

Inequalities tend to have infinitely many solutions.

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.

They can have none, one or infinitely many.

None, one or infinitely many

When there is an ordered pair that satisfies both inequalities.

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

Inequalities are defining part of the plane So either they intersect in infinitely many point (either in a part of the plane or on a line) or they don't intersect 1 - zero solution x+y > 1 and x+y <0 2 - infinitely many solution x+y >2 and x + y > 3 (a part of the plane) x+y >=2 and x+y <= 2 (a line)

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.

yes

There is only one solution set. Depending on the inequalities, the set can be empty, have a finite number of solutions, or have an infinite number of solutions. In all cases, there is only one solution set.

No. For example, the solution to x â‰¤ 4 and x â‰¥ 4 is x = 4.

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

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