Systems of Linear Inequalities in Two Variables

6.2

Systems of Linear Inequalities in Two Variables

	Definition

	A combination of two or more linear inequalities

Table below shows an appropriate inequality for a certain situation.

Example of situation		Linear inequality

\(y\) is greater than \(x\)		\(y>x\)

\(y\) is less than \(x\)		\(y < x \)

\(y\) is not less than \(x\)		\(y\geq x\)

\(y\) is not more than \(x\)		\(y\leq x\)

\(y\) is at least \(k\) times \(x\)		\(y\geq kx\)

\(y\) is at most \(k\) times \(x\)		\(y\leq kx\)

Maximum of \(y\) is \(k\)		\(y\leq k\)

Minimum of \(y\) is \(k\)		\(y\geq k\)

Sum of \(x\) and \(y\) is greater than \(k\)		\(x+y >k \)

Difference between \(y\) and \(x\) is less than \(k\)		\(y-x

\(y\) is more than \(x\) by at least \(k\)		\(x-y \geq k \)