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Do solutions to systems of linear inequalities satisfy both inequalities?
Yes.
Must solutions to systems of linear inequalities satisfy both inequalities?
Yes.
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.
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.
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.
Do solutions to systems of linear inequalities satisfy both inequalities?
Yes.
Must solutions to systems of linear inequalities satisfy both inequalities?
Yes.
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.
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.
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.
What does it mean to describe all of the numbers that satisfy both inequalities?
I assume you have inequalities that involve variables. If you replace the variable by some number, you will get an inequality that is either true or false. A value for the variable that results in a true statement is said to "satisfy" the inequality. For example, in: x + 3 > 10 If you replace x by 8, you get a true statement, since 11 is greater than 10; if you replace x by 7, you get a false statement, since 10 is not greater than 10. In this case, there are two inequalities; you have to find all numbers that satisfy both inequalities; in other words, that convert both inequalities into true statements.
What graph represents the solution set of this system of inequalities?
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.
What are multi step inequalities?
Multi-step inequalities are mathematical statements that involve inequalities with more than one operation to solve for a variable. They typically require several steps, such as adding, subtracting, multiplying, or dividing, while also applying the rules of inequalities, such as reversing the inequality sign when multiplying or dividing by a negative number. These inequalities can represent a range of values for the variable that satisfy the given condition. Solving multi-step inequalities helps in understanding relationships and constraints in various mathematical and real-world contexts.
Is satisfying an equation the same as solving it?
No. If an equation has many solutions, any one of them will satisfy it.
What do you call the set of solutions that satisfy a given equation?
That's called the "solution set".
What does intersection mean mathiticaly?
The intersection is the set of solutions that satisfy two or more mathematical expressions.
How are compound inequalities used in real life?
Compound inequalities are used in real life to describe ranges of values that satisfy multiple conditions simultaneously. For example, a restaurant may require customers to be aged between 18-65 years old and have a minimum income of $30,000 to qualify for a discount. In this case, compound inequalities can help determine who meets both criteria.
