Notesale: Turn your study into money

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• Now, multiply first equation by 1; multiply the second equation by 4
• The system then becomes:
o 8𝑥 + 4𝑦 = 12
o −8𝑥 + 4𝑦 = 36
• Note that both equations contain the term 4𝑦

SOLUTION USING ELIMINATION METHOD
• Now subtract the second equation from first equation :
• 8𝑥 + 4𝑦 − −8𝑥 + 4𝑦 = 12 − 36

• This yields 16𝑥 = −24, ∴ 𝑥 = −1
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5 into any of the equations above (let’s choose the second

equation here):
• −2(1
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• Plug this expression for 𝑧 into the second and third equations:

• 2nd equation: 2𝑥 − 𝑦 − 𝑥 + 𝑦 + 4 = 0 ⇒ 𝑥 − 2𝑦 − 4 = 0
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• Rewrite 𝑥 − 2𝑦 − 4 = 0 i
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o
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• Plug 𝑦 = 4 into 𝑥 = 2𝑦 + 4 → 𝑥 = 2 4 + 4 ;
• ∴ 𝑥 = 12
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(1)
o 2𝑥 − 𝑦 − 𝑧 = 0
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(3)
• Let’s decide to get rid of 𝑥 first
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The result
is:
• 2𝑥 + 2𝑦 − 2𝑧 = −8 (a) and
• 2𝑥 − 𝑦 − 𝑧 = 0 (b)

ELIMINATION 2
• Subtract (b) from (a):
• 2𝑥 + 2𝑦 − 2𝑧 − 2𝑥 − 𝑦 − 𝑧 = −8 − 0 ⟹ 3𝑦 − 𝑧 = −8

• Now, multiply (1) by 3 and (3) by 1
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(1a)

• 3𝑥 − 4𝑦 − 𝑧 = 0
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(4)
o 7𝑦 − 2𝑧 = −12
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The result is
• 21𝑦 − 7𝑧 = −56
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(5a)

ELIMINATION 3
• Now subtract (5a) from (4a):
• 21𝑦 − 7𝑧 − 21𝑦 − 6𝑧 = −56 − (−36)

• This gives: −𝑧 = −20,
• ∴ 𝑧 = 20

• Then 𝑦 = 4 and 𝑥 = 12 which is the same as the result found using
substitution
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• Demand of goods and services is based on the theory of consumer behaviour
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• Demand function: Relationship between quantity demanded and price,
• e
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𝑞 𝑑 = 𝑏 − 𝑎𝑝
• The negative sign on 𝑎 means that as price increase quantity demanded decreased
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• Supply function: relationship between quantity supplied and price,
• e
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𝑞 𝑠 = 𝑐𝑝 + 𝑑
• The positive sign on 𝑐 means that as price increase quantity supplied increase
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DEMAND AND SUPPLY FUNCTION - Figure 3
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(Graphically??)

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