1) Replace the inequality signs in the solution and in the original question with = signs. Substitute the solution inn the question: it should make it true.
2) (Back to the inequalities) Pick another number that satisfies the solution inequality - e.g. if x>2, pick 5. Substitute this into the original inequality: if it makes it true, then you are good to go!
It depends on whether the inequalities are strict or not.
An inequality determines a region of space in which the solutions for that particular inequality. For a system of inequalities, these regions may overlap. The solution set is any point in the overlap. If the regions do not overlap then there is no solution to the system.
yes
The solution to a system of inequalities is where the solutions to each of the individual inequalities intersect. When given a set of graphs look for the one which most closely represents the intersection, this one will contain the most of the solution to the the system but the least extra.
the answer is true
Check all of the inequalities.
Which system of inequalities has a solution set that is a line?
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.
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.
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.
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.
true
It depends on whether the inequalities are strict or 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.
To determine the graph that represents the solution set of a system of inequalities, you need to plot each inequality on a coordinate plane. The solution set will be the region where the shaded areas of all inequalities overlap. Typically, the boundaries of the inequalities will be represented by solid lines (for ≤ or ≥) or dashed lines (for < or >). Identifying the correct graph involves checking which regions satisfy all the inequalities simultaneously.
Thanks to the browser, it is not possible to tell what the inequalities are.