Download 第二學習階段

Key Stage 3
Number and Algebra Dimension
Learning Unit： Linear Equations in Two Unknowns
Learning Objectives：
• plot and explore the graphs of linear equations in 2 unknowns
• formulate and solve simultaneous equations by algebraic and
graphical methods
• be aware of the approximate nature of the graphical method
Programme Title: Simultaneous Equations
Programme Objectives
1.
2.
3.
4.
5.
Recognize the graphs and solutions of linear equations in 2 unknowns.
Understand the graphical solutions of simultaneous equations.
Solve simultaneous equations by the method of substitution.
Solve simultaneous equations by the method of elimination.
Solve practical problems of simultaneous equations.
Programme Content
In considering the number of different gift boxes of tea, the idea of the solutions
of linear equations in two unknowns is introduced. It points out that there is not
a unique solution for a linear equation in two unknowns as the possible
solutions are the dots on a straight line in the coordinate plane.
The programme uses the inter-crossing station of the KCR and MTR route to
bring forth the idea of the graphical solution of simultaneous equations. The
unique solution is given by the point of intersection of the two straight line
graphs.
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In the discussion of solving a problem of mixing two kinds of tea, the
procedures of solving problems of simultaneous equations are introduced:
Step (1): Use letters to represent unknowns.
Step (2): Use given conditions to form equations.
Step (3): Solve equations (graphical, substitution or elimination).
Step (4): Check solution.
It also points out the approximate nature of the graphical solutions and thus
introduces the algebraic methods, substitution and elimination, for solving
simultaneous equations to obtain accurate solutions.
Worksheet Answers
1. 6；
solution is: y  3.75 and x  1.25；
the solution is the same as that of the programme.
2. It is more convenient to substitute y from equation (2) into equation (1)
so as to avoid fractional expressions, or to eliminate y to form a linear
equation in x so as to avoid multiplying both equations by numbers.
(some of the possible answers).
Solution is: x  5 and y  2.
3. Let Kitty had x correct answers and y wrong answers.
therefore,
xy  25
4xy  65；
Solution the equations: x  18 and y  7. That is, Kitty had 18 correct
answers and 7 wrong answers.
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Key Stage 3 ETV Programme
《Linear Equations in Two Unknowns》
Worksheet
1. In the programme, when solving the simultaneous equations:
6x 2y  15 ……… (1)
x y  5 ……… (2)
the unknown y is eliminated to obtain a linear equation in one unknown, x,
and then the solution: x1.25 and y3.75 is obtained.
If now we want to eliminate the unknown x,
then what number should be multiplied to equation (2)?
From this, find the solution of the simultaneous equations and compare it
with that of the programme.
Therefore, the solution *is/is not the same as that of the programme.
(*delete whatever inappropriate)
2. Solve the simultaneous equations:
7x 13y  9 ……… (1)
3x y  17 ……… (2)
Which method would you use, graphical, substitution or elimination? Why?
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Use the method you selected to solve the equations.(If you select the
graphical method, use your own graph paper).
3. Follow the four steps as proposed in the programme to solve the following
problem in simultaneous equations:
A multiple choice question test has 25 questions. 4 marks are given
to a correct answer and 1 mark is deducted for a wrong answer.
Kitty scored 65 marks in the test. How many correct answers and
how many wrong answers did she get?
Step 1
Use letters to represent
unknowns
Step 2
Use given conditions to
form equations
Step 3
Use
appropriate
method
to
solve
equations (graphical,
substitution
or
elimination)
Step 4
Check solution
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