Download 2.4.Linear Relations

Chapter 8: Homework
Homework: Linear relations
Section A
1 For each of the following pairs of linear functions sketch their graphs on the same set of axes
to determine the point of intersection.
a y=5
b y = 2x – 3
c y=x–3
d x–y=4
y = 2x – 1
y=x+2
y = –2x
2x – y = 2
2 Solve each of the simultaneous equations graphically.
a y = 2x + 1
b x+y=2
c x – y = –4
x = –2
x – y = –2
4x – y = 2
d x + y = –1
3x + y = –5
3 A company manufactures toys. Its costs, rent, materials labour etc. are given by the rule
C = n + 5000 and its revenue, R by the rule R = 2n where n is the number of toys produced.
Sketch the graph of C and R on the same set of axes and determine the point where the cost
is equal to the revenue.
4 Solve each of the following simultaneous linear equations by using substitution.
a x+y=3
b 2x + y = 5
c 5x – 3y = 1
d y=x+8
y=4
x=1
y = 2x
y = –3x
5 Solve each of the following simultaneous linear equations by using substitution.
a x+y=6
b 4x – y = 3
c 2x – y = 3
d x + y = –1
y=x+2
y=2–x
y = 3x + 4
x = 2y + 5
6 Solve each of the following simultaneous linear equations by using substitution.
a 2x + 3y = 7
b 2x – 4y = 6
c 3x + 5y = 12
d 2x – 3y = –3
y = 5 – 2x
x = 3y – 3
y=x–4
x=6–y
Section B
7 Solve the following simultaneous linear equations by using elimination.
a x+y=1
b 3x + 2y = –3
c 4x – y = –2
d 2x + y = 6
x–y=5
x – 2y = –9
3x – y = 6
x+y=4
8 Solve the following simultaneous linear equations by using elimination.
a 2x + 3y = –6
b x + y = –8
c 3x – 5y = 3
d 6x – 2y = 2
x–y=2
3x – 2y = –4
x – 4y = 8
x – 3y = –5
9 Solve the following simultaneous linear equations by using elimination.
a 3x – 2y = 8
b 3x – 5y = –4
c 4x – 3y = 2
d 5x –3y = –4
2x – 3y = 2
5x – 4y = 2
3x – 2y = –4
3x – 4y = 2
10 The sum of two numbers is 18 and the difference between them is 8. Find the two numbers.
11 The length of a rectangle is 8cm longer than its width. If the perimeter is 68cm fine the
dimensions of the rectangle.
12 The entry cost to see a Phoenix Netball match is $15 for adults and $9 for children. A total of
$15 000 was collected from the 1200 people who saw the match. Find the number of adults
and the number of children who saw the match.
13 Harry bought six pens and two rulers for $14. Ben bought eight pens and four rulers for $20.
Find the cost of a pen and the cost of a ruler.
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E ssenti al Maths 9 © C ambri dge U ni versi ty P ress 2003
Chapter 8: Homework
14 Two years ago a mother was six times as old as her daughter. In four years she will be three
times as old as daughter. Find the mother’s and daughter’s present age.
15 The rates charged by two electricians to rewire a house are shown below.
Wireit:
Powerit:
$1000 plus $175 per day
$1475 plus $80 per day
a Write a rule for the cost, C1 of using Wireit’s services.
b Write a rule for the cost, C2 of using Powerit’s services.
c Sketch the graphs of C1 and C2 on the same set of axes and determine how long a job needs
to take for the cost of either electrician to be the same.
d Check your answer to part (c) algebraically.
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E ssenti al Maths 9 © C ambri dge U ni versi ty P ress 2003
Chapter 8: Homework Answers
Homework Answers
Section A
Section B
1 a (3, 5)
c (1, –2)
b (5, 7)
d (–2, –6)
7 a (3, –2)
c (–8, –30)
b (–3, 3)
d (2, 2)
2 a (–2, –3)
c (2, 6)
b (0, 2)
d (–2, 1)
8 a (0, –2)
c (–4, –3)
b (–4, –4)
d (1, 2)
9 a (4, 2)
c (–16, –22)
b (2, 2)
d (–2, –2)
3 (5000, 10 000)
4 a (–1, 4)
c (–1, –2)
b (1, 3)
d (–2, 6)
5 a (2, 4)
c (–7, –17)
b (1, 1)
d (1, –2)
6 a (2, 1)
c (4, 0)
b (15, 6)
d (3, 3)
10 5, 13
11 13 cm × 21 cm
12 700 adults and 500 children
13 $2 (pen), $1 (ruler)
14 26 (mother), 6 (daughter)
15 a C1 = 1000 + 175d
b C2 = 1475 + 80d
c 5 days
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E ssenti al Maths 9 © C ambri dge U ni versi ty P ress 2003