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.
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.
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.
The answer depends on which area is shaded for each inequality. I always teach pupils to shade the unwanted or non-feasible region. That way the solution is in the unshaded area. This is much easier to identify than do distinguish between a region which is shaded three times and another which is shaded four times.
Check all of the 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.
They make up the 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.
Unless otherwise stated, the "AND" case is normally assumed, i.e., you have to find a solution that satisfies ALL equations.
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.
The answer depends on which area is shaded for each inequality. I always teach pupils to shade the unwanted or non-feasible region. That way the solution is in the unshaded area. This is much easier to identify than do distinguish between a region which is shaded three times and another which is shaded four times.
Check all of the inequalities.
Linear algebraic inequalities can be described as an expression with a variable >/< an expression with a variable. For example, 2x<90 so x<45. Inequalities don't yield a particular solution, but rather solution sets. In the above example, x<45, means that the solution set is all of the values less than 45.
I am not at all convinced that it is. With more than three variables it is almost impossible and even with 3 variables, it is hard going.
its true because they have all have the same linear pair It's actually false
the solution for the inequality 4x + 2 - 6x < -1 was x < 3/2
It is called the "soulltion set"