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Mathematics

Assertion(A): 2m+3m=0 and 23m+2n=16\dfrac{2}{m} + \dfrac{3}{m} = 0 \text{ and } \dfrac{2}{3m} + \dfrac{2}{n} = \dfrac{1}{6} is a pair of simultaneous linear equations.

Reason(R): An equation of the form ax + by + c = 0, a ≠ 0, b ≠ 0 is called linear equations in two variables.

  1. A is true, R is false

  2. A is false, R is true

  3. Both A and R are true

  4. Both A and R are false

Linear Equations

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Answer

Given,

Equations: 2m+3m=0 and 23m+2n=16\dfrac{2}{m} + \dfrac{3}{m} = 0 \text{ and } \dfrac{2}{3m} + \dfrac{2}{n} = \dfrac{1}{6}

⇒2m+3m=0⇒5m=0⇒5=0×m⇒5≠0.\Rightarrow \dfrac{2}{m} + \dfrac{3}{m} = 0 \\[1em] \Rightarrow \dfrac{5}{m} = 0 \\[1em] \Rightarrow 5 = 0 \times m \\[1em] \Rightarrow 5 \ne 0 .

Since 5 is not equal to 0, this equation has no solution for m. We cannot find values for m and n that satisfy both equations simultaneously.

⇒23m+2n=16\Rightarrow \dfrac{2}{3m} + \dfrac{2}{n} = \dfrac{1}{6} Again, this is not linear in variables m and n, because the variables are in denominators.

Assertion (A) is false.

An equation of the form ax + by + c = 0, a ≠ 0, b ≠ 0, is called a linear equation in two variables.

Reason(R) is true.

A is false, R is true

Hence, option 2 is the correct option.

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