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Is it possible for a system of two linear inequalities to have no solution and be parallel?
Wiki User
∙ 9y ago
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
Wiki User
∙ 9y ago
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When is system of linear inequalities have no solution?
When the lines never intersect, usually when they are parallel.
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.
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?
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.
Do solutions to systems of linear inequalities need to satisfy linear inequalities?
No. For example, the solution to x ≤ 4 and x ≥ 4 is x = 4.
Is it possible for a system of two linear inequalities to ha a single point as a solution?
yes it is possible for a system of two linear inequalities to have a single point as a solution.
When is system of linear inequalities have no solution?
When the lines never intersect, usually when they are parallel.
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.
Can the solution of a system of linear inequalities be the points on a line?
yes
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?
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.
Do solutions to systems of linear inequalities need to satisfy linear inequalities?
No. For example, the solution to x ≤ 4 and x ≥ 4 is x = 4.
Is it possible to have a system of linear inequalities where solution is every point in the entire?
Yes, you can say something like y < infinity and y > -infinity .
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
How do you know which region of the graph of a system of linear inequalities contains the solutions?
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.
What is a linear equation with no solution?
Parallel
A system of two linear inequalities has either no points or infinitely many points in its solution?
the answer is true
