Tell whether the following statement is true or false:
The following pair of linear equations are consistent.
$32 x + 53 y = 7$ ; 9x-10 y=14

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True

False

answer is A.

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Detailed Solution

Given two equations

32 x + 53 y = 7

and 9x – 10y = 14.
We have to first find out the coefficient of both equations, by comparing with ax+by+c=0.

32 x + 53 y = 7 ⇒ 9 x + 10 y 6 = 7 ⇒ 9 x + 10 y = 42

For equation

9 x + 10 y = 42

a 1 = 9, b 1 = 10 and c 1 = − 42

For equation 9x – 10y = 14,

a 2 = 9, b 2 = − 10 and c 2 = − 14

Now, finding their ratios

a 1 a 2 = 99 = 1

b 1 b 2 = 10 − 10 = − 1

c 1 c 2 = − 42 − 14 = 3

Comparing the ratios,

a 1 a 2 ≠ b 1 b 2 1 ≠ − 1

Since all ratios are different, the line has only one solution.
Therefore, the equations are consistent.
The given statement is true.
Hence, option 1 is correct.

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