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Mathematics

Assertion (A): (2x - 3y, 8) = (2, x + 2y)
⇒ x = 1 and y = -2

Reason (R): 2x - 3y = 2 and x + 2y = 8
Solving we get : x = 4 and y = 2

  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.

Coordinate Geometry

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Answer

A is false, R is true.

Explanation

Given, (2x - 3y, 8) = (2, x + 2y)

So, 2x - 3y = 2 and x + 2y = 8

Multiplying 2 in second equation and subtracting from first equation, we get,

2x−3y=22x+4y=16−−−−7y=2−16⇒−7y=−14\begin{matrix} & 2x & - & 3y & = & 2 \ & 2x & + & 4y & = & 16 \ & - & - & & & - \ \hline & & - & 7y & = & 2 - 16 \ \Rightarrow & & - & 7y & = & -14 \end{matrix}

⇒ y = 147\dfrac{14}{7} = 2

Putting the value y = 2 in first equation,

⇒ 2x - 3 x 2 = 2

⇒ 2x - 6 = 2

⇒ 2x = 2 + 6

⇒ 2x = 8

⇒ x = 82\dfrac{8}{2} = 4

According to Assertion, x = 1 (≠ 4) and y = -2 (≠ 2)

∴ Assertion (A) is false.

From the above calculation, x = 4 and y = 2.

∴ Reason (R) is true.

Hence, Assertion (A) is false, Reason (R) is true.

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