Tell whether the following statement is true or false:
The following pair of linear equations are consistent.
2x - 3y = 8; 4x - 6y = 9

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True

False

answer is B.

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Detailed Solution

Given two linear equations 2x - 3y = 8 and 4x - 6y = 9.
We have to first find out the coefficient of both equations,
For equation 2x - 3y = 8,

a 1 = 2, b 1 = − 3 and c 1 = − 8

For equation 4x - 6y = 9,

a 2 = 4, b 2 = − 6 and c 2 = − 9

Now, finding their ratios,

a 1 a 2 = 24 = 12

b 1 b 2 = − 3 − 6 = 12

c 1 c 2 = − 8 − 9 = 89

Comparing the ratios,

a 1 a 2 = b 1 b 2 ≠ c 1 c 2 12 = 12 ≠ 89

Since, first pair is equal and other is not, the lines are parallel and have no solutions.
Therefore, the equations are inconsistent.
The correct statement is that the given pair of linear equations is inconsistent.
The given statement is false.
Hence, option 2 is correct.

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