Using simultaneous equation to solve problems

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Using simultaneous equation to solve problems
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Problem Solving With Simultaneous Equations
Example The problem
For the cinema
2 adults tickets and 5 childrens tickets cost
26
4 adults tickets and 2 children tickets cost 28
Find the cost of each kind of ticket.
Introduce Letters
Let the cost of adult ticket A
Let the cost of childrens ticket C
Write the equations
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Solve the Problem using simultaneous equations
Conclusion Adult Ticket costs 5.50 Children's
tickets cost 3
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strategy

1. Read the problem
2. Introduce two letters
3. Write two equations that describe the information
4. Solve the problem using simultaneous equations
5. check

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Substitution method
This an excellent method of solving simultaneous
equations when the equations are given to you in
a certain form
Solve the equations y 2x and y x 10
Example 1
We take the equation y x 10
And substitute 2x for y
2x x 10
Take out y and replace it with 2x
x 5
Sub x5 into y2x
y 10
Now solve the equation
Solution x 5 y 10
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Example 2
Solve the equations y 2x 8 and y x 1
Sub y 2x-8 in the equation
y - x 1
2x 8 -x 1
x 8 1
x 9
y 18-8
Sub x 9 in the equation y 2x -8
y 10
Solution x 9 and y 10
Check 10 9 1
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Problems with simultaneous equations from past
papers

• 1. The tickets for a sports club cost 2 for
  members and 3 for non- members
• The total ticket money collected was 580
• x tickets were sold to members and y
  tickets were sold to non-members.
• Use this information to write down an equation
  involving x and y

2x 3y 580
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b) 250 people bought raffle tickets for the
disco. Write down another equation involving x
and y.
x y 250
c ) How many tickets were sold to members ?
We now have two equations in x and y so lets
solve them simultaneously
2x 3y 580 x y 250
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2x 3y 580 x y 250
X 1
X (-2)
2x 3y 580 -2x (-2 )y
-500
ADD
y 80
Sub y 80 into x y 250
check
x 80 250
2 x170 3x80 340 240 580
x 170
170 tickets were sold to members
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2. Alloys are made by mixing metals.Two
different alloys are made using iron and lead. To
make the first alloy, 3 cubic cms of iron and 4
cubic cms of lead are used.
This alloy weighs 65 grams
a ) Let x grams be the weight of 1 cm3 f
iron and y grams be the weight of 1 cm3 of lead
Write down an equation in x and y which
satisfies the above equation.
3x 4 y 65
To make the second alloy, 5 cm3 of iron and
7cm3 of lead are used . This alloy weighs
112 grams.
b ) Write down a second equation in x and y which
satisfies this condition
5x 7y 112
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C ) Find the weight of 1 cm3 of iron and the
weight of 1cm3 of lead.
X (-5)
3x 4 y 65 5x 7y 112
X 3
Check 5x7 7x11 35 77 112
-15x -20 y -325 15x 21y 336
ADD
y 11
y 11 into 3x 4y 65
SUB
3x 44 65
1cm3 of iron weighs 7gms and 1cm3 of lead
weighs 11 gms
3x 21
x 7
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3. A rectangular window has length , l cm and
breadth, b cm .




A security grid is made to fit this window. The
grid as 5 horizontal wires and 8 vertical wires
a ) The perimeter of the window is 260 cm. Use
this information to write down an equation
involving l and b .
2 l 2 b 260
b) In total, 770 cm of wire is used. Write down
another equation involving l and b
5 l 8 b 770
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Find the length and breadth of the window
2 l 2 b 260 5 l 8 b 770
X (4)
X (-1)
8 l 8 b 1040 -5 l (-8) b
-770
ADD
3 l 270 l 90
5x90 8x40 450 320770
l 90 into 2 l 2 b 260
SUB
180 2b 260
Length is 90cm and the breadth is 40 cm
2b 80
b 40