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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.

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Q: What are the solutions to system of inequalities?

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The definition of equivalent inequalities: inequalities that have the same set of solutions

If the equations or inequalities have the same slope, they have no solution or infinite solutions. If the equations/inequalities have different slopes, the system has only one solution.

Yes.

Yes.

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.

If it is joined by an "and" it does. If it is joined by an "or" it does not.

The solution to a system of inequalities is where the solutions to each of the individual inequalities intersect. When given a set of graphs look for the one which most closely represents the intersection, this one will contain the most of the solution to the the system but the least extra.

If the lines intersect, then the intersection point is the solution of the system. If the lines coincide, then there are infinite number of the solutions for the system. If the lines are parallel, there is no solution for the system.

Yes, they can.

To find the solutions.

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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.

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