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Question

If x,y and z are real numbers such that 4x+2y+z=31 and 2x+4y−z=19, then the value of 9x+7y+z

A
equals 1823
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B
equals 2183
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C
equals 2813
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D
cannot be computed from the given information
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Solution

The correct option is B equals 2183
Let 9x+7y+z=a(4x+2y+z)+b(2x+4yz)
Then 9x+7y+z=(4a+2b)x+(2a+4b)y+(ab)z
Comparing the coefficients, we get
4a+2b=9 (1)
2a+4b=7 (2)
ab=1 (3)
Solving (1) and (2),
a=116,b=56
(116,56) also satisfies (3).

9x+7y+z=116(4x+2y+z)+56(2x+4yz)
=116×31+56×19=2183

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