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A system of two linear inequalities has either no points or infinitely many points in its solution?
the answer is true
which graph shows the solution to the system of linear inequalities y>2x+1 y?
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What is inconsistent system of linear equation?
It is a system of linear equations which does not have a solution.
Can the solution of a system of linear inequalities be the point of a line explain?
It's pretty much always the point of a line because the soulution of the system is always an ordered pair where the two or more lines intersect
How is the solution in a system of inequalities determine?
An inequality determines a region of space in which the solutions for that particular inequality. For a system of inequalities, these regions may overlap. The solution set is any point in the overlap. If the regions do not overlap then there is no solution to the system.
A system of two linear inequalities has either no points or infinitely many points in its solution?
the answer is true
What is the difference between the solution of a system of linear inequalities and the solution of a system of linear equations?
The solution of a system of linear equations consists of specific points where the equations intersect, typically yielding a unique point, infinitely many points, or no solution at all. In contrast, the solution of a system of linear inequalities represents a region in space, encompassing all points that satisfy the inequalities, often forming a polygonal shape in two dimensions. While equations define boundaries, inequalities define areas that can include multiple solutions. Thus, the nature of their solutions differs fundamentally: precise points versus expansive regions.
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
When does A system of two linear inequalities have a solution?
When there is an ordered pair that satisfies both inequalities.
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.
Why is the solution of a system of linear inequalities the intersection?
The solution of a system of linear inequalities is the intersection of the individual inequalities because each inequality represents a region in the coordinate plane. The intersection includes only the points that satisfy all the inequalities simultaneously, meaning they fall within all the defined regions. This ensures that any solution point meets the criteria set by each inequality in the system. Thus, the intersection effectively captures the set of solutions that are valid for the entire system.
When is it possible for a system of two linear inequalities to have no solution?
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.
How would you know if the solutions you found from the graphs of linear inequalities in a system are true?
To verify the solutions of a system of linear inequalities from a graph, check if the points satisfy all the inequalities in the system. You can do this by substituting the coordinates of each point into the original inequalities to see if they hold true. Additionally, ensure that the points lie within the shaded region of the graph, which represents the solution set. If both conditions are met, the solutions are confirmed to be true.
When is system of linear inequalities have no solution?
When the lines never intersect, usually when they are parallel.
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.
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.
