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Mathematics

Assertion: If 9 is the value of variable x in the equation 2x−72=y\dfrac{2x - 7}{2} = y, then the value of y is 28.

Reason: The value which when substituted for the variable in an equation, makes LHS = RHS is called a solution of the given equation.

  1. Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
  2. Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).
  3. Assertion (A) is true but Reason (R) is false.
  4. Assertion (A) is false but Reason (R) is true.

Linear Eqns One Variable

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Answer

Assertion (A) is false but Reason (R) is true.

Explanation

Assertion:

Given equation:

2x−72=y\dfrac{2x - 7}{2} = y

Substitute x = 9 into the equation:

=2x−72=y⇒2(9)−72=y⇒18−72=y⇒112=y5.5=y\phantom{=} \dfrac{2x - 7}{2} = y \\[1em] \Rightarrow \dfrac{2(9) - 7}{2} = y \\[1em] \Rightarrow \dfrac{18 - 7}{2} = y \\[1em] \Rightarrow \dfrac{11}{2} = y \\[1em] 5.5 = y

Since y = 5.5 and not 28, the Assertion is False.

Reason:

The definition provided for a "solution" or "root" of an equation is mathematically perfect. Therefore, the Reason is True.

Hence, option 4 is the correct option.

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