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How many solutions does two linear inequalities have?
None, one or infinitely many
Can the solution of a system of linear inequalities be the points on a line?
yes
How are quadratic inequalities different from linear inequalities?
A linear inequality is all of one side of a plane. A quadratic inequality is either the inside of a parabola or the outside.
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.
How many solutions are there to a linear inequality?
Infinitely many. The solution space is part of a plane.
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 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 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.
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.
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.
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
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 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?
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.
