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