# Solving equations booklet

```Equations and inequalities
Equations and inequalities
Topic 3: Two-step equations
QUESTION 1
a
d
g
Solve the following two-step equations.
2x + 7 = 17 _______________ c
9y – 4 = 23 _____________
________________________
________________________
_______________________
6a – 5 = 25 _______________ e
8a + 7 = 47 _______________ f
3m
5 = 6 _______________
________________________
________________________
_______________________
3x – 1 = 5 _______________
x–3
5 = 4 _______________
QUESTION 2
b
h
3x + 8 = 32 ______________
a
3 – 2 = 9 _______________
5x – 5 = 30 ______________
b
a
e
h
2y + 5 = 35 ______________
5t – 2 = 8 ______________
3y + 2 = 5 ______________
x–3
4 = 6 ______________
________________________
50
4a – 2&middot;5 = 9&middot;5 ____________
x
2 + 7 = 12 ______________
7p – 8 = 13 ____________
_______________________
f
6a + 112 = 412 ____________
_______________________
i
x–3
2 = 8 _______________
_______________________
Solve these equations.
b
7y – 3 = 4 ______________
c
________________________
e
m–3
4 = 5 ______________
h
5y – 4 = 26 _____________
f
2y + 8 = –2 ______________
2x – 1 = 17 _____________
_______________________
i
________________________
k
8x – 6 = 26 ______________
_______________________
________________________
________________________
j
c
________________________
________________________
g
8y – 3 = 21______________
________________________
________________________
d
3x – 2 = 19 _____________
_______________________
________________________
________________________
QUESTION 3
i
Solve the following equations.
________________________
g
a
2 – 4 = 6 _______________
________________________
________________________
d
page 151
UNIT 3: Two-step equations
________________________
a
2x – 5 = 11 ____________
_______________________
l
________________________
4p – 6 = –10 ____________
_______________________
EXCEL ESSENTIAL SKILLS: YEAR 10 MATHEMATICS REVISION AND EXAM WORKBOOK 1
Equations and Inequalities
Mathletics Instant Workbooks – Series K
3
Simultaneous
Simultaneousequations
equations
page 161
UNIT 2: The substitution method
Topic 2: The substitution method
QUESTION 1 Solve the following pairs of simultaneous equations by substitution.
a
c
e
b
x+y=6
x–y=4
2x + 3y = 6
x – 3y = 12
_______________________________________
_______________________________________
_______________________________________
_______________________________________
_______________________________________
_______________________________________
_______________________________________
_______________________________________
x – 4y = 16
–x + 8y = 12
d
x + 5y = 8
2x – 5y = 4
_______________________________________
_______________________________________
_______________________________________
_______________________________________
_______________________________________
_______________________________________
_______________________________________
_______________________________________
3m + 4n = 12
m + 4n = 4
f
2p + 5q = 7
p – 4q = 36
_______________________________________
_______________________________________
_______________________________________
_______________________________________
_______________________________________
_______________________________________
_______________________________________
_______________________________________
QUESTION 2 Use the method of substitution to solve the following pairs of simultaneous equations.
a
c
114
b
2x + y = 7
3x – 2y = 14
x + 3y = 9
x – 3y = 3
_______________________________________
_______________________________________
_______________________________________
_______________________________________
_______________________________________
_______________________________________
_______________________________________
_______________________________________
4x – 5y = 14
x + 2y = 23
d
x + 2y = 8
3x – y = 24
_______________________________________
_______________________________________
_______________________________________
_______________________________________
_______________________________________
_______________________________________
_______________________________________
_______________________________________
EXCEL ESSENTIAL SKILLS: YEAR 10 MATHEMATICS REVISION AND EXAM WORKBOOK 1
Simultaneous equations
Mathletics Instant Workbooks – Series K
2
Simultaneous equations
Simultaneous equations
page 161
UNIT 4: The elimination method
Topic 4: The elimination method
QUESTION 1 Solve the following pairs of simultaneous equations by the method of elimination.
a
c
e
x + 3y = 4
x – 3y = 10
_______________________________________
_______________________________________
_______________________________________
_______________________________________
2a + 5b = 8
3a – 5b = 7
_______________________________________
_______________________________________
_______________________________________
_______________________________________
a+b=7
a–b=9
_______________________________________
_______________________________________
_______________________________________
_______________________________________
b
d
f
5x – 2y = 11
3x + 2y = 5
_______________________________________
_______________________________________
_______________________________________
_______________________________________
3x – y = 5
8x + y = 6
_______________________________________
_______________________________________
_______________________________________
_______________________________________
4x + 7y = 14
3x – 7y = 7
_______________________________________
_______________________________________
_______________________________________
_______________________________________
QUESTION 2 Use the method of elimination to solve the following pairs of simultaneous equations.
a
c
e
116
x + 3y = 12
x – 5y = 4
_______________________________________
_______________________________________
_______________________________________
_______________________________________
2a + 5b = 16
2a – 3b = –8
_______________________________________
_______________________________________
_______________________________________
_______________________________________
3x + 8y = 12
3x – 2y = 2
_______________________________________
_______________________________________
_______________________________________
_______________________________________
b
d
f
12m + 5n = 45
3m + 5n = 9
_______________________________________
_______________________________________
_______________________________________
_______________________________________
5x + 2y = 15
3x + 2y = 9
_______________________________________
_______________________________________
_______________________________________
_______________________________________
4m + 9n = 15
2m + 9n = 7
_______________________________________
_______________________________________
_______________________________________
_______________________________________
EXCEL ESSENTIAL SKILLS: YEAR 1- MATHEMATICS REVISION AND EXAM WORKBOOK 1
Simultaneous equations
Mathletics Instant Workbooks – Series K
4
Simultaneous equations
Simultaneous equations
page 161
UNIT 5: Elimination method involving different coefficients
Topic 5: Elimination method involving different coefficients
QUESTION 1 Solve the following pairs of simultaneous equations by the method of elimination.
a
c
e
2x + 3y = 6
x–y=3
_______________________________________
_______________________________________
_______________________________________
_______________________________________
3a + 5b = 6
2a + b = 4
_______________________________________
_______________________________________
_______________________________________
_______________________________________
5x – 2y = 7
3x + y = 2
_______________________________________
_______________________________________
_______________________________________
_______________________________________
b
d
f
4x + 7y = 8
x–y=2
_______________________________________
_______________________________________
_______________________________________
_______________________________________
4m – 5n = –14
2m + 3n = 4
_______________________________________
_______________________________________
_______________________________________
_______________________________________
2a – 5b = 3
5a – 2b = –3
_______________________________________
_______________________________________
_______________________________________
_______________________________________
QUESTION 2 Use the method of elimination to solve the following pairs of simultaneous equations.
a
c
e
3x + y = 5
x + 3y = 7
_______________________________________
_______________________________________
_______________________________________
_______________________________________
x + 3y = 18
2x – 4y = 6
_______________________________________
_______________________________________
_______________________________________
_______________________________________
2x + 3y = 1
4x – y = 9
_______________________________________
_______________________________________
_______________________________________
_______________________________________
b
d
f
2m + n = 6
3m – 2n = 2
_______________________________________
_______________________________________
_______________________________________
_______________________________________
4x + 9y = 4
3x – y = 3
_______________________________________
_______________________________________
_______________________________________
_______________________________________
5x + 2y = 2
–x + 3y = 3
_______________________________________
_______________________________________
_______________________________________
_______________________________________
117
Chapter 10: Simultaneous equations
Simultaneous equations
Mathletics Instant Workbooks – Series K
5
Simultaneous
Simultaneousequations
equations
page 162
UNIT 6: Using simultaneous equations to solve worded problems
Topic 6: Using simultaneous equations to solve worded problems
QUESTION 1
a
The sum of two numbers is 35 and their difference is 19. Find the numbers. ________________________
______________________________________________________________________________________
______________________________________________________________________________________
______________________________________________________________________________________
b
The sum of two numbers is 72. Twice the first number minus the second number is equal to 54.
Find the numbers. ______________________________________________________________________
______________________________________________________________________________________
______________________________________________________________________________________
______________________________________________________________________________________
There are 840 students in a school. If there are 120 more girls than boys, how many boys and girls are
there? ________________________________________________________________________________
______________________________________________________________________________________
______________________________________________________________________________________
______________________________________________________________________________________
The difference between the length and width of a rectangular room is 8 m and the perimeter of the room
is 64 m. Find the length and width of the room. _______________________________________________
______________________________________________________________________________________
______________________________________________________________________________________
______________________________________________________________________________________
c
d
QUESTION 2
a
Four apples and five oranges cost \$3.20 whereas two apples and three oranges cost \$1.80.
Find the price of each piece of fruit. ________________________________________________________
______________________________________________________________________________________
______________________________________________________________________________________
______________________________________________________________________________________
b
Maddie is four years older than her brother Angus. If the sum of their ages is 30 years, what are their
ages? _________________________________________________________________________________
______________________________________________________________________________________
______________________________________________________________________________________
______________________________________________________________________________________
Suzie is four times as old as her daughter Samantha. The sum of their ages is 70 years. Find their ages.
______________________________________________________________________________________
______________________________________________________________________________________
______________________________________________________________________________________
______________________________________________________________________________________
c
118
EXCEL ESSENTIAL SKILLS: YEAR 10 MATHEMATICS REVISION AND EXAM WORKBOOK 1
Simultaneous equations
Mathletics Instant Workbooks – Series K