We've looked at solving simultaneous equations using the substitution method and the elimination method. Now we are going to look at how to solve two inequalities simultaneously.

The process is just the same as solving a simultaneous. However, all the same rules apply that we learnt regarding inequalities if we need to change the subject of an inequality.

Remember!

If we multiply or divide both sides of an inequality by a negative number, the inequality symbol reverses direction.

Examples

Question 1

In an office building, an elevator has a maximum carrying capacity of $12750$12750 pounds. This is based on an average female's weight of $150$150 pounds and an average male's weight of $170$170 pounds.

Let $x$x represent the number of women who enter the elevator.

Let $y$y represent the number of men who enter the elevator.

Write an inequality to represent the number of men and women who can enter the elevator at one time, with $y$y as the subject.

Question 2

Caitlin has experimented with growing two types of banana trees. She has found that the two types grow optimally if Type A takes up no more than $30%$30% of the plantation area and Type B takes up at least $20%$20% of the plantation area.

Let $x$x and $y$y represent the proportion (expressed as decimals) of Type A and Type B banana trees planted respectively.

State the system of three inequalities representing the restrictions on $x$x and $y$y. Write the inequalities on the same line, separated by a comma. Represent all values as decimals.