Inequalities and Simultaneous Equations

Question 1

How do you solve inequalities?

Answer 1

Same as normal equations - what you do to one side you do to the other.

Question 2

What happens if you multiply or divide by a negative number?

Answer 2

The inequality changes direction.

Question 3

How do you find a solution which satisfies two inequalities?

Answer 3

Solve them both separately and combine them or write them in set notation.

Question 4

What is it important not to do when solving quadratic inequalities and why?

Answer 4

Divide or multiply by variables as it may be negative or it could equal 0.

Question 5

How do you find the set of values that satisfies both a quadratic and linear inequality?

Answer 5

Work out the solution of each inequality separately and then use a graph to help you find the solution that satisfies both.

Question 6

How do you show regions on a graph that satisfy inequalities in two variables (x and y)?

Answer 6

1. Write each inequality as an equation (change the inequality to and equals).
2. Draw the graph for each equation.
3. Work out which side of each line you want.
4. Label the correct region.

Question 7

How do you solve simultaneous equations?

Answer 7

Find one of the variables as an expression of the other, substitute it into the other equation and solve for the remaining variable. Once you have one variable, use it to find the other.