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Question

2a(2pq)=1,
p=2q1
Consider the system of equations above, where a is a constant. For which value of a is (p,q)=(1,1) a solution?

A

2

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B
12
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C
12
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D
None of the above
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Solution

The correct option is B 12
[Beware of option D we need to check whether given values satisfy the system ]
We should first substitute (1, 1) in to the second equation to see it (1, 1) is a possible solution
p=2q1
1=2(1)1
1 = 1

Because the second equation created a true statement, we proceed by substituting (1, 1) into the first equation.
2a(2(1)1)=1
2a(21)=1
2a=1
a=12

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