Yes.
Yes.
No. For example, the solution to x ≤ 4 and x ≥ 4 is x = 4.
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.
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.
If it is joined by an "and" it does. If it is joined by an "or" it does not.
Yes.
No. For example, the solution to x ≤ 4 and x ≥ 4 is x = 4.
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.
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.
If it is joined by an "and" it does. If it is joined by an "or" it does not.
They can have none, one or infinitely many.
In a graph of a system of two linear inequalities, the doubly shaded region represents the set of all points that satisfy both inequalities simultaneously. Any point within this region will meet the criteria set by both linear inequalities, meaning its coordinates will fulfill the conditions of each inequality. Consequently, this region illustrates all possible solutions that satisfy the system, while points outside this region do not satisfy at least one of the inequalities.
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.
A set of two or more inequalities is known as a system of inequalities. This system consists of multiple inequalities that involve the same variables and can be solved simultaneously to find a range of values that satisfy all conditions. Solutions to a system of inequalities are often represented graphically, where the feasible region indicates all possible solutions that meet all the inequalities. Such systems are commonly used in linear programming and optimization problems.
A system of linear inequalities give you a set of answers that could work. In day to day lives we actually use linear inequalities all the time. We are given questions and problems where we search for a number of possible solutions.
Any solution to a system of linear equations must satisfy all te equations in that system. Otherwise it is a solution to AN equation but not to the system of 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.