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A system of two linear inequalities can have no solution when the inequalities represent parallel lines that do not intersect. This occurs when the lines have the same slope but different y-intercepts. In such cases, there is no set of values that can satisfy both inequalities simultaneously, resulting in an empty solution set.
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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.
When is system of linear inequalities have no solution?
When the lines never intersect, usually when they are parallel.
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 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.
What are the solutions to system of inequalities?
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.
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 does A system of two linear inequalities have a solution?
When there is an ordered pair that satisfies both inequalities.
Can the solution of a system of linear inequalities be the points on a line?
yes
When is system of linear inequalities have no solution?
When the lines never intersect, usually when they are parallel.
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 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.
A system of two linear inequalities has either no points or infinitely many points in its solution?
the answer is true
When solving a system of linear inequalities what does the region that is never shaded represent?
It represents the solution set.
What are the solutions to system of inequalities?
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.
What consists of 2 or more linear inequalities in the same variable?
A system of linear inequalities
which graph shows the solution to the system of linear inequalities y>2x+1 y?
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