Tell whether the following statement is true or false:
The following pair of linear equations are consistent.

3x + 2y = 5; 2x - 3y = 7

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True

False

answer is A.

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Detailed Solution

Given 2 linear equations 3x + 2y = 5 and 2x - 3y = 7.
According to the question,
We have to first find out the coefficient of both equations by comparing with ax+by+c=0.
The equations are,
3x + 2y = 5 ----- 1
2x - 3y = 7 ----- 2
For equation 1,

a 1 = 3, b 1 = 2 and c 1 = − 5

For equation 2,

Now, finding their ratios,

a 1 a 2 = 32

b 1 b 2 = 2 − 3 b 1 b 2 = − 23

c 1 c 2 = − 5 − 7 c 1 c 2 = 57

Comparing the ratios,

a 1 a 2 ≠ b 1 b 2 32 ≠ − 23

Since, the ratios are not equal, the equations are consistent.
The given statement is true.
Hence, option 1 is correct.

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