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Mathematics

Assertion (A): Solutions of equations 3y - 2x = 1 and 3x + 4y = 24 is x = 4 and y = 3.

Reason (R): ∵ 3y - 2x = 3 x 3 - 2 x 4 = 1 and, 3x + 4y = 3 x 4 + 4 x 3 = 24

  1. A is true, but R is false.

  2. A is false, but R is true.

  3. Both A and R are correct, and R is the correct explanation for A.

  4. Both A and R are correct, and R is correct explanation for A.

Linear Equations

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Answer

If x = 4 and y = 3 are the solution of equation 3y - 2x = 1, then substitute x = 4 and y = 3 in L.H.S. and R.H.S., both values should be same.

Given,

3y - 2x = 1

Substituting value of x and y in L.H.S. of the above equation, we get :

⇒ 3y - 2x

⇒ 3 x 3 - 2 x 4

⇒ 9 - 8

⇒ 1

As, L.H.S. = R.H.S.

So, x = 4 and y = 3 are the solution of equation 3y - 2x = 1.

3x + 4y = 24

Substituting value of x and y in L.H.S. of the equation :

⇒ 3x + 4y

⇒ 3 x 4 + 4 x 3

⇒ 12 + 12

⇒ 24

As, L.H.S. = R.H.S.

So, x = 4 and y = 3 are the solution of equation 3x + 4y = 24.

∴ Both A and R are correct, and R is the correct explanation for A.

Hence, option 3 is the correct option.

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