No it is NOT always bounded. Here is an example of an unbounded one. 1. 2x-y>-2 2. 4x+y
yes it is possible for a system of two linear inequalities to have a single point as a solution.
It represents the solution set.
A system of linear inequalities
Yes, you can say something like y < infinity and y > -infinity .
A linear equation corresponds to a line, and a linear inequality corresponds to a region bounded by a line. Consider the equation y = x-5. This could be graphed as a line going through (0,-5), (1,-4), (2,-3), and so on. The inequality y > x-5 would be the region above that line.
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.
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.
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 ≤ 4 and x ≥ 4 is x = 4.
In question and answer logic answers are given and if they fall in an area bounded by the inequality then it is a good answer. After graphing three or more inequalities the vertexes are the possible maxima of the system of equations.
When the lines never intersect, usually when they are parallel.
the answer is true
It represents the solution set.
Inequalities tend to have infinitely many solutions.
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.