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Mathematics

If 4[5x]5[y2]=[1022]4\begin{bmatrix}[r] 5 & x \end{bmatrix} - 5\begin{bmatrix}[r] y & -2 \end{bmatrix} = \begin{bmatrix}[r] 10 & 22 \end{bmatrix}, the values of x and y are :

  1. x = 2 and y = 3

  2. x = 3 and y = 2

  3. x = -3 and y = 2

  4. x = 3 and y = -2

Matrices

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Answer

Given,

4[5x]5[y2]=[1022][204x][5y10]=[1022][205y4x(10)]=[1022][205y4x+10]=[1022]\Rightarrow 4\begin{bmatrix}[r] 5 & x \end{bmatrix} - 5\begin{bmatrix}[r] y & -2 \end{bmatrix} = \begin{bmatrix}[r] 10 & 22 \end{bmatrix} \\[1em] \Rightarrow \begin{bmatrix}[r] 20 & 4x \end{bmatrix} - \begin{bmatrix}[r] 5y & -10 \end{bmatrix} = \begin{bmatrix}[r] 10 & 22 \end{bmatrix} \\[1em] \Rightarrow \begin{bmatrix}[r] 20 - 5y & 4x - (-10) \end{bmatrix} = \begin{bmatrix}[r] 10 & 22 \end{bmatrix} \\[1em] \Rightarrow \begin{bmatrix}[r] 20 - 5y & 4x + 10 \end{bmatrix} = \begin{bmatrix}[r] 10 & 22 \end{bmatrix}

∴ 20 - 5y = 10 and 4x + 10 = 22

⇒ 5y = 20 - 10 and 4x = 22 - 10

⇒ 5y = 10 and 4x = 12

⇒ y = 2 and x = 3.

Hence, Option 2 is the correct option.

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