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Answer to Q82
A - 4B + 2C = 16, 2A + 7B - 5C = 83. What is A + B - C?
A - 4B + 2C = 16 (eqn i)
2A + 7B - 5C = 83 (eqn ii)
A + B - C (eqn iii)
Multiply (eqn i) by 2
2A - 8B + 4C = 32 (eqn iv)
Subtract (eqn ii) from (eqn iv)
-15B + 9C = -51
C = (-51 + 15B) ÷ 9 (eqn v)
Putting (eqn v) into (eqn i)
A - 4B - (102 ÷ 9) + (30B ÷ 9) = 16
A = 16 + 4B + (102 ÷ 9) - (30B ÷ 9) (eqn vi)
Putting (eqn vi) and (eqn v) into (eqn iii)
16 + 4B + (102 ÷ 9) - (30B ÷ 9) + B + (51÷ 9) - (15B ÷ 9)
Making 9 the common factor
(144 + 36B - 30B + 102 + 9B + 51 - 15B) ÷ 9
297 ÷ 9
= 33
Answer: 33
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