Maths Quest 10 for New South Wales 5.3 Pathway
Work Programs
Chapter 8
Simultaneous equations
Strand: Patterns and algebra
Substrands and outcomes:
Algebraic techniques
PAS4.3 Uses the algebraic symbol system to simplify, expand and factorise simple algebraic expressions
Algebraic techniques
PAS4.4 Uses algebraic techniques to solve linear equations and simple inequalities
Algebraic techniques
PAS5.2.2 Solves linear and simple quadratic equations, solves linear inequalities and solves simultaneous
equations using graphical and analytical methods
Algebraic techniques
PAS5.3.2 Solves linear, quadratic and simultaneous equations, solves and graphs inequalities, and
rearranges literal equations
Coordinate geometry
PAS5.2.3 Uses formulae to find midpoint distance and gradient and applies the gradient/intercept form
to interpret and graph straight lines
Coordinate geometry
PAS5.3.3 Uses various standard forms of the equation of a straight line and graphs regions on the number
plane
Curve sketching and polynomials
PAS5.3.6 Uses a variety of techniques to sketch a range of curves and describes the features of curves from
the equation
Section
Are you ready? (page 290)
GC tips, Investigations,
History of mathematics,
Maths Quest challenge,
10 Quick Questions,
Code puzzles,
Career profiles
SkillSHEETS,
WorkSHEETS,
Interactive games,
Test yourself, Topic tests
(CD ROM)
SkillSHEETs (page 290)
8.1: Solving linear
1
Technology applications
(CD ROM)
Learning outcomes
PAS4.4
 solving equations arising
equations that arise
when finding x- and yintercepts
8.3: Finding the gradient
of a line from its
equation
8.4: Transposing linear
equations to make x or y
the subject
8.6: Writing equations
from worded statements
8.7: Checking solutions to
inequalities
Introduction (page 291)
Solving simultaneous
equations using nonalgebraic methods
(page 292)
Graphical solution of
simultaneous equations
(page 294)
WE 1, 2, 3
Ex 8A Graphical solution
of simultaneous
equations (page 298)
Investigation: Solving
simultaneous equations
using tables of values
(page 292)
Investigation: Solving
simultaneous equations
using guess, check and
improve (page 293)
GC tip – Casio: Solving
simultaneous equations
graphically (page 297)
Investigation: How many
cockatoos and
kangaroos? (page 300)
SkillSHEET 8.1: Solving
linear equations that
arise when finding xand y- intercepts
(page 299)
SkillSHEET 8.2: Graphing
linear equations using
the x- and y-intercept
method (page 299)
SkillSHEET 8.3: Finding
the gradient of a line
from its equation
(page 300)
Game time 001 (page 300)
2
GC tip – TI: Solving
simultaneous equations
graphically (page 297)
Mathcad: Simultaneous
equations – graphical
(page 298)
Excel: Simultaneous
equations – graphical
(page 298)
from substitution into
formulae
 checking solutions by
substituting
PAS5.2.3
 recognising equations of
the form y  mx  b as
representing straight
lines and interpreting the
x-coefficient (m) as the
gradient
PAS5.3.2
 changing the subject of a
formula
PAS4.3
 translating from
everyday language to
algebraic language
PAS5.2.2
 solving simultaneous
equations using nonalgebraic methods, such
as ‘guess and check’,
setting up tables of
values or looking for
patterns
 solving linear
simultaneous equations
by finding the point of
intersection of their
graphs
 using graphics
calculators and
spreadsheet software to
plot pairs of lines and
Algebraic solutions of
simultaneous equations
– substitution method
(page 301)
WE 4, 5, 6
Ex 8B Algebraic solutions
of simultaneous
equations – substitution
method (page 304)
Algebraic solutions of
simultaneous equations
– elimination method
(page 306)
WE 7, 8
Ex 8C Algebraic solutions
of simultaneous
equations – elimination
method I (page 307)
Maths Quest challenge
Q1-5 (page 304)
10 Quick Questions 1
(page 305)
Further use of the
elimination method
(page 308)
WE 9, 10
Ex 8D Algebraic solutions
of simultaneous
equations – elimination
method 2 (page 310)
GC tip – Casio: Solving
simultaneous equations
using the equations
function (page 309)
Maths Quest challenge
Q1-2 (page 310)
Code puzzle (page 311)
Investigation: Cramer’s
rule for simultaneous
equations (page 312)
Investigation:
Simultaneous equations
in 3 unknowns
SkillSHEET 8.4:
Mathcad: Simultaneous
Transposing linear
equations – substitution
equations to make x or y
(page 304)
the subject (page 304)
Excel: Simultaneous
Game time 002 (page 304)
equations – substitution
WorkSHEET 8.1
(page 304)
(page 304)
reading off the point of
intersection (Applying
strategies)
PAS5.2.2
 solving simple linear
simultaneous equations
using an analytical
method
SkillSHEET 8.5: Addition
and subtraction of
simultaneous equations
(page 307)
Mathcad: Simultaneous
equations – elimination
(page 308)
Excel: Simultaneous
equations ax + by = c
form (page 308)
PAS5.2.2
 solving simple linear
simultaneous equations
using an analytical
method
WorkSHEET 8.2
(page 310)
GC tip – TI: Solving
simultaneous equations
using the equations
function (page 309)
Excel: Simultaneous
equations – elimination
(page 310)
PAS5.2.2
 solving simple linear
simultaneous equations
using an analytical
method
 solving linear
simultaneous equations
resulting from problems
and interpreting the
results (Applying
strategies,
Communicating)
3
Problem solving using
simultaneous equations
(page 313)
WE 11, 12
Ex 8E Problem solving
using simultaneous
equations (page 315)
(page 312)
Investigation: Concert hall
seating (page 317)
10 Quick Questions 2
(page 318)
Maths Quest challenge
Q1-3 (page 318)
SkillSHEET 8.6: Writing
equations from worded
statements (page 315)
Solving a quadratic
equation and a linear
equation
simultaneously
(page 319)
WE 13, 14, 15
Ex 8F Solving a quadratic
equation and a linear
equation
simultaneously
(page 322)
Excel: Simultaneous
equations (page 315)
GC program TI:
Simultaneous equations
(page 315)
Mathcad: simultaneous
equations – quadratic
and linear (page 322)
Excel: simultaneous
equations – quadratic
and linear (page 322)
4
PAS5.2.2
 generating simultaneous
equations from simple
word problems
 solving linear
simultaneous equations
resulting from problems
and interpreting the
results (Applying
strategies,
Communicating)
PAS5.3.2
 using analytical methods
to solve a variety of
simultaneous equations,
including those that
involve a first degree
equation and a second
degree equation
 explaining why a
particular value could
not be a solution to an
equation (Applying
strategies, Reasoning,
Communicating)
 graphing simultaneous
equations to find
solutions and comparing
this method with
analytical methods
(Applying strategies,
Reflecting,
Communicating)
PAS5.3.6
Solving simultaneous
inequalities (page 323)
WE 16
Ex 8G Solving
simultaneous
inequalities (page 326)
SkillSHEET 8.7: Checking
solutions to inequalities
(page 326)
SkillSHEET 8.8: Checking
whether a given point
makes the inequality a
true statement
(page 326)
SkillSHEET 8.9: Shading
half planes to
demonstrate linear
inequalities (page 326)
WorkSHEET 8.3
(page 329)
5
GrafEq (page 325)
 determining the points of
intersection of a line
with a parabola
graphically and
algebraically
PAS5.3.2
 using <, >, , ,  to
generate linear
inequalities from
problems
PAS5.3.3
 graphing inequalities of
the form y < a, y > a, y
 a, y  a, x > a, x  a
and x  a on the number
plane
 graphing inequalities
such as y  x on the
number plane by
considering the position
of the boundary of the
region as the limiting
case
 checking whether a
particular point lies in a
given region specified by
a linear inequality
 graphing regions such as
that specified by
x+y<7
2x  3y  5
 describing the region
from a graph by
identifying the boundary
lines and determining the
appropriate inequalities
for describing the
enclosed region
(Applying strategies,
Communicating)
Summary (page 330)
Chapter review (page 331)
‘Test yourself’ multiple
choice questions
Topic tests (2)
6