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Do two linear inequalities have zero or one or several or infinitely many solutions?
Inequalities are defining part of the plane
So either they intersect in infinitely many point (either in a part of the plane or on a line) or they don't intersect
1 - zero solution
x+y > 1 and x+y <0
2 - infinitely many solution
x+y >2 and x + y > 3 (a part of the plane)
x+y >=2 and x+y <= 2 (a line)
What else can I help you with?
How many solutions do systems of linear inequalities have?
They can have none, one or infinitely many.
How many solution does a linear inequality in one variable have?
Inequalities tend to have infinitely many solutions.
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.
Do solutions to systems of linear inequalities satisfy both inequalities?
Yes.
Must solutions to systems of linear inequalities satisfy both inequalities?
Yes.
How many solutions does two linear inequalities have?
None, one or infinitely many
How many solutions do systems of linear inequalities have?
They can have none, one or infinitely many.
How many solution does a linear inequality in one variable have?
Inequalities tend to have infinitely many solutions.
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.
Do solutions to systems of linear inequalities satisfy both inequalities?
Yes.
Must solutions to systems of linear inequalities satisfy both inequalities?
Yes.
Do solutions to systems of linear inequalities need to satify both inequalities?
If it is joined by an "and" it does. If it is joined by an "or" it does not.
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.
A system of two linear inequalities has either no points or infinitely many points in its solution?
the answer is true
How many solutions does linear equation in two variable have?
A single linear equation in two variables has infinitely many solutions. Two linear equations in two variables will usually have a single solution - but it is also possible that they have no solution, or infinitely many solutions.
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.
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.
