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Question

Which of the following equations are consistent?

A
2x+4y=11; 2x+4y=23
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B
7xy=5; 14x2y=4
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C
x+y=7; 2xy=8
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D
xy=5; 2x2y=11
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Solution

The correct option is C x+y=7; 2xy=8
Pair of equations is said to be consistent if they have at least one solution i.e., one or infinite solutions.
The pair of equations mentioned in options A, B and D has no solution as they are parallel lines. Pair of equations mentioned in C are:

x+y=7 ....(i)
2xy=8 ....(ii)

Here, a1=1,b1=1,c1=7
a2=2,b2=1,c2=8

1211
The pair of linear equations given in option C, is consistent and has a unique solution.

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