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Solve (A^-1 + B)X = C for x and y, A and B given 2x2 matrices

The same question, asked 2 times: 18 Apr 2026 S1*, 13 May 2026 S2. Every wording below, oldest first.

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  1. Question 1

    18 Apr 2026 S1

    66
    Let A=[3−41−1]A = \begin{bmatrix} 3 & -4 \\ 1 & -1 \end{bmatrix} and B=[6−135−10]B = \begin{bmatrix} 6 & -13 \\ 5 & -10 \end{bmatrix} be two matrices. If the variables xx and yy satisfy the matrix equation ((A−1)2+B)[xy]=[00]((A^{-1})^2 + B)\begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 0 \\ 0 \end{bmatrix}, then the ordered pair (x,y)=(x, y) =

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  2. Question 2

    13 May 2026 S2

    69
    Let A=[2132]A = \begin{bmatrix} 2 & 1 \\ 3 & 2 \end{bmatrix} and B=[−1−111]B = \begin{bmatrix} -1 & -1 \\ 1 & 1 \end{bmatrix}. If the variables xx and yy satisfy the matrix equation (A−1+B)[xy]=[0−2](A^{-1} + B)\begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 0 \\ -2 \end{bmatrix}, then the value of x+3yx + 3y is......

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