Linear Inequalities in Two Variables

6.1

Linear Inequalities in Two Variables

Inequalities are used to describe the relationship between two quantities that are not equal.

	Example

	Anne wants to buy some revision books and exercise books at a book exhibition. She finds that the price of a reference book is \(\text{RM}15\) and the price of exercise book is \(\text{RM}10\). The maximum amount of money that Anne can spend is \(\text{RM}100\). Represent the above situation in an appropriate form of linear inequality.

	Solution: Let's \(x= \text{reference book}\), \(y= \text{exercise book}\). Thus, \(15x + 10 y\leq100\) or \(10y \leq100-15x\)

Inequality can also be represented on a Cartesian plane by shading the region that satiesfies inequality.

Relationship between a point on a Cartesian plane with the inequality \(y >mx +c, y < mx+c, y \geq mx+c, \text{or}, y\leq mx+c\)


\(>,<\)		Points that lie in the region above or below a straight line \(y=mx+c\)

		The straight line is drawn using a dashed line

\(\geq, \leq\)		Points that lie on the straight line\(y=mx +c\) including the region above or below

		The straight line is drawn using a solid line

6.1

Linear Inequalities in Two Variables

Inequalities are used to describe the relationship between two quantities that are not equal.

	Example

	Anne wants to buy some revision books and exercise books at a book exhibition. She finds that the price of a reference book is \(\text{RM}15\) and the price of exercise book is \(\text{RM}10\). The maximum amount of money that Anne can spend is \(\text{RM}100\). Represent the above situation in an appropriate form of linear inequality.

	Solution: Let's \(x= \text{reference book}\), \(y= \text{exercise book}\). Thus, \(15x + 10 y\leq100\) or \(10y \leq100-15x\)

Inequality can also be represented on a Cartesian plane by shading the region that satiesfies inequality.

Relationship between a point on a Cartesian plane with the inequality \(y >mx +c, y < mx+c, y \geq mx+c, \text{or}, y\leq mx+c\)


\(>,<\)		Points that lie in the region above or below a straight line \(y=mx+c\)

		The straight line is drawn using a dashed line

\(\geq, \leq\)		Points that lie on the straight line\(y=mx +c\) including the region above or below

		The straight line is drawn using a solid line