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Are there more potential solutions to systems of inequalities in a half-plane or in the entire plane?
Wiki User
∙ 11y ago
There are more solutions in a half plane
Wiki User
∙ 11y ago
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What does it mean by solving linear systems?
Solving linear systems means to solve linear equations and inequalities. Then to graph it and describing it by statical statements.
Systems of equations have one solution?
Systems of equations can have just about any number of solutions: zero, one, two, etc., or even infinitely many solutions.
How do you solve systems of inequalities?
first look and see if you graphed the lines between the two and the slope is m and the y-int is b .
Do all linear quadratic systems have two solutions or one?
They will have 2 different solutions or 2 equal solutions and some times none depending on the value of the discriminant within the quadratic equation
When equations of linear systems have different slopes how many solutions does it have?
One 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.
How many solutions do systems of linear inequalities have?
They can have none, one or infinitely many.
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.
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 liniear inequalities need to satisfy both inequalitites?
Yes. There are lots of answers that will satisfy each.
Why are systems of linear inequality so important?
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.
Can some systems of inequalities have no solution?
true
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.
Why is graphing a systems of inequalities a good way to show the solution set?
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