Chapter 15: Inequalities and
Systems of Inequalities
Inequalities are statements about the relative size or order of
two objects, and systems of inequalities involve multiple
inequalities that must be satisfied simultaneously. This chapter
explores solving systems of inequalities and their graphical
representation, as well as real-world applications.
Solving Systems of Inequalities
A system of inequalities consists of two or more inequalities
that share the same variables. Solving such a system involves
finding all sets of values that satisfy all the inequalities at once.
The solution is often represented as a region on a coordinate
plane, showing the area where all the inequalities overlap.
For example, consider the system: -
\[ \begin{align*}
x + 2y &\leq 6 \\
x - y &\geq 1
\end{align*} \]
To solve it, each inequality is graphed on the same coordinate
plane, and the solution is the area where the shaded regions of
both inequalities intersect.
Systems of Inequalities
Inequalities are statements about the relative size or order of
two objects, and systems of inequalities involve multiple
inequalities that must be satisfied simultaneously. This chapter
explores solving systems of inequalities and their graphical
representation, as well as real-world applications.
Solving Systems of Inequalities
A system of inequalities consists of two or more inequalities
that share the same variables. Solving such a system involves
finding all sets of values that satisfy all the inequalities at once.
The solution is often represented as a region on a coordinate
plane, showing the area where all the inequalities overlap.
For example, consider the system: -
\[ \begin{align*}
x + 2y &\leq 6 \\
x - y &\geq 1
\end{align*} \]
To solve it, each inequality is graphed on the same coordinate
plane, and the solution is the area where the shaded regions of
both inequalities intersect.
