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When does A system of two linear inequalities have a solution?
When there is an ordered pair that satisfies both inequalities.
How many solution sets do systems of linear inequalities have Must solutions to systems of linear inequalities satisfy both inequalities In what case might they not?
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.
True or false a system of two linear inequalities has either no points or infinity many points in a solution?
its true because they have all have the same linear pair It's actually false
Is it possible for a system of two linear inequalities to have exactly one solution?
Yes. As a simple example, consider X ≥ 1 and x ≤ 1. They have the one solution: x = 1
Is it possible for a system of two linear inequalities to have no solution and be parallel?
Yes, it is possible. Since their boundaries are parallel the relevant equations are of the form y = mx + c1 and y = mx + c2. Then if c1 > c2, the inequalities must be of the form y ≥ mc + c1 and y ≤ mx + c2
