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Mathematics

If [x+34y4x+y]=[5439]\begin{bmatrix}[r] x + 3 & 4 \ y - 4 & x + y \end{bmatrix} = \begin{bmatrix}[r] 5 & 4 \ 3 & 9 \end{bmatrix}, find the values of x and y.

Matrices

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Answer

Given [x+34y4x+y]=[5439]\begin{bmatrix}[r] x + 3 & 4 \ y - 4 & x + y \end{bmatrix} = \begin{bmatrix} 5 & 4 \ 3 & 9 \end{bmatrix}.

By definition of equality of matrices, we get

    x + 3 = 5, y - 4 = 3 and x + y = 9
⇒ x = 2, y = 7 and x + y = 9.

Note that x = 2 and y = 7 satisfies the equation x + y = 9.

Hence, the value of x = 2 and y = 7.

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