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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 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 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.
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
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 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.
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
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
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
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
Is it true that Every system of inequalities in two variables has at least one solution?
No.
What system of two linear equations in two variables that has exactly one solution?
An independent system has one solution.
What is the solution of a system of linear equations in two variables?
The solution of a system of linear equations is a pair of values that make both of the equations true.
Is the graph of a solution set of a system of two linear inequalities always bounded?
No it is NOT always bounded. Here is an example of an unbounded one. 1. 2x-y>-2 2. 4x+y
Does every system of a linear equation have a solution?
No, if two lines are parallel they will not have a solution.
Why a system of linear equations cannot have exactly two solutions?
A system of linear equations can only have: no solution, one solution, or infinitely many solutions.
