true
Not every system of inequalities has a solution. A system of inequalities can be inconsistent, meaning that there are no values that satisfy all inequalities simultaneously. For example, the inequalities (x < 1) and (x > 2) cannot be satisfied at the same time, resulting in no solution. However, many systems do have solutions, which can be represented as a feasible region on a graph.
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.
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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.
No. For example, the solution to x ≤ 4 and x ≥ 4 is x = 4.
Not every system of inequalities has a solution. A system of inequalities can be inconsistent, meaning that there are no values that satisfy all inequalities simultaneously. For example, the inequalities (x < 1) and (x > 2) cannot be satisfied at the same time, resulting in no solution. However, many systems do have solutions, which can be represented as a feasible region on a graph.
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.
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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.
No. For example, the solution to x ≤ 4 and x ≥ 4 is x = 4.
Which system of inequalities has a solution set that is a line?
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.
Yes.
Yes.
If the equations or inequalities have the same slope, they have no solution or infinite solutions. If the equations/inequalities have different slopes, the system has only one solution.
When there is an ordered pair that satisfies both inequalities.
If it is joined by an "and" it does. If it is joined by an "or" it does not.