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Mathematics

If [x+34y−4x+y]=[5439],\begin{bmatrix}[r] x + 3 & 4 \ y - 4 & x + y \end{bmatrix} = \begin{bmatrix}[r] 5 & 4 \ 3 & 9 \end{bmatrix}, then the values of x and y are

  1. x = 2, y = 7
  2. x = 7, y = 2
  3. x = 3, y = 6
  4. x = -2, y = 7

Matrices

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Answer

Given,

[x+34y−4x+y]=[5439]\begin{bmatrix}[r] x + 3 & 4 \ y - 4 & x + y \end{bmatrix} = \begin{bmatrix}[r] 5 & 4 \ 3 & 9 \end{bmatrix} \\[0.5em]

By definition of equality of matrices we get,

⇒ x + 3 = 5 or x = 5 - 3 = 2.

⇒ y - 4 = 3 or y = 3 + 4 = 7.

⇒ x + y = 9.

Since, x = 2 and y = 7 satisfies the equation x + y = 9, hence, value of x = 2 and y = 7.

∴ Option 1 is the correct option.

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