Chapter 3 Equations and Inequalities

Question 1

which techniques can be used to solve linear simultaneous equations?

Answer 1

• elimination
• substitution

Question 2

what do the solutions to a pair of simultaneous equations represent on a graph?

Answer 2

the points of intersection of their graphs

Question 3

what is the solution of an inequality equivalent to?

Answer 3

the set of all real numbers that make the equality true

Question 4

how do you solve a quadratic inequality?

Answer 4

• rearrange so that the right side of the inequality is 0
• solve the corresponding quadratic equation to find the critical values
• sketch the graph of the quadratic function and use it to find the required set of values

Question 5

which values of x satisfy the inequality f(x) < g(x)?

Answer 5

the values of x for which the curve y = f(x) is below the curve y = g(x)

Question 6

which values of x satisfy the inequality f(x) > g(x)?

Answer 6

the values of x for which the curve y = f(x) is above the curve y = g(x)

Question 7

what does y < f(x) represent on a graph?

Answer 7

the points below the curve y = f(x)

Question 8

what does y > f(x) represent on a graph?

Answer 8

the points above the curve y = f(x)

Question 9

what is the line for y > f(x) and y < f(x)?

Answer 9

dotted as the curve y = f(x) isnt included in the region

Question 10

what is the line for y > or = to f(x) and y < or = to f(x)?

Answer 10

solid as the curve y = f(x) is included in the region