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Chapter 5: Problem 94

What is a solution of a system of linear inequalities?

Short Answer

Expert verified
A solution of a system of linear inequalities is an ordered pair, or set of values, that makes all the inequalities in the system true at the same time.

Step by step solution

01

Understanding the concept of linear inequalities

A linear inequality is a mathematical statement that relates a linear expression as either less than, greater than, less than or equal to, greater than or equal to another linear expression. For example, \(2x + 3y \leq 6\) is a linear inequality.
02

Defining a system of linear inequalities

A system of linear inequalities comprises two or more linear inequalities involving the same set of variables. For example, \(\begin{cases} 2x + 3y \leq 6 \ x - y > 1 \end{cases}\) forms a system of two linear inequalities in two variables \(x\) and \(y\).
03

Understanding a solution to a system of linear inequalities

A solution to a system of linear inequalities is any ordered pair of numbers that satisfy all the inequalities in the system simultaneously. In other words, if you plug the values of the solution into every inequality of the system, they should all hold true. This means if you were to graph each inequality on a coordinate plane, the regions where all the inequalities overlap form the solution set.

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Most popular questions from this chapter

Determine whether each statement makes sense or does not make sense, and explain your reasoning. Because the percentage of the U.S. population that was foreign-born decreased from 1910 through 1970 and then increased after that, a quadratic function of the form \(f(x)=a x^{2}+b x+c,\) rather than a linear function of the form \(f(x)=m x+b,\) should be used to model the data.

write the partial fraction decomposition of each rational expression. $$ \frac{1}{x^{2}-c^{2}} \quad(c \neq 0) $$

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I'm solving a three-variable system in which one of the given equations has a missing term, so it will not be necessary to use any of the original equations twice when I reduce the system to two equations in two variables.

write the partial fraction decomposition of each rational expression. $$ \frac{a x+b}{x^{2}-c^{2}} \quad(c \neq 0) $$

Solve by the addition method: $$ \left\\{\begin{array}{l} 2 x+4 y=-4 \\ 3 x+5 y=-3 \end{array}\right. $$
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