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In 2-dimensional space, an equality could be represented by a line. A set of equalities would be represented by a set of lines. If these lines intersected at a single point, that point would be the solution to the set of equations.

With inequalities, instead of a line you get a region - one side of the line representing the corresponding equality (or the other). The line, itself, may be included or excluded. Each inequality can be represented by a region and, if these regions overlap, any point within that sub-region is a solution to the system of inequalities.

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Q: What does it mean to find the solutions of system of inequalities?

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It means that however many different solutions (answers) you have, there will always be more solutions that can be proven, and you can never find them all.

No. At least, it can't have EXACTLY 3 solutions, if that's what you mean. A system of two linear equations in two variables can have:No solutionOne solutionAn infinite number of solutions

Instead of using y = mx + b you use y (inequality sign) mx + b. By inequality sign, I mean symbols like

Your question asks about "each inequalities" which is grammatically impossible since "each" implies singular whereas inequalities implies plural. Consequently it is not clear whether you mean "each inequality" or "each of a set of inequalities". In either case the set is called the feasible region, or the 2-dimensional solution set.

Solving linear systems means to solve linear equations and inequalities. Then to graph it and describing it by statical statements.

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Compound inequalities is when there is two inequality signs. You will regularly graph compound inequalities on a number line.

Inequalities are less than, equal to, less than or equal to, or more than or equal to. Inequalities can NOT contain an equal sign.

this means you have no more than 5 solutions in a system of equations.

It means that however many different solutions (answers) you have, there will always be more solutions that can be proven, and you can never find them all.

No. At least, it can't have EXACTLY 3 solutions, if that's what you mean. A system of two linear equations in two variables can have:No solutionOne solutionAn infinite number of solutions

It means that both inequalities must be satisfied.

Instead of using y = mx + b you use y (inequality sign) mx + b. By inequality sign, I mean symbols like

It means that there is no set of values for the variables such that all the linear equations are simultaneously true.

Your question asks about "each inequalities" which is grammatically impossible since "each" implies singular whereas inequalities implies plural. Consequently it is not clear whether you mean "each inequality" or "each of a set of inequalities". In either case the set is called the feasible region, or the 2-dimensional solution set.

Lots of equations or inequalities can have infinitely many solutions. That means that the set of solutions is not finite; if you were to try to list the individual solutions, you would never end. In inequalities, the situation is quite clear; if the solution to an inequality is of the form: x > 10 then there are infinitely may solutions (11, 12, 13, 14, 15, ... but also 10.1, 10.2, 10.01, 15.073, etc.); and if you try to write out each solution, you would never get done. This is also possible with equations, in the case of periodic functions; for example: sin x = 0 has the solutions (0, 180°, 360°, 540°, ...), or in radians (0, pi, 2 pi, 3 pi, 4 pi, ...) due to the fact that the sine function is periodic.

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.

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