Determine x + y if \(\begin{pmatrix} 2 & -3 \\ -1 & 4 \end{pmatrix}\) \(\begin{pmatrix} x \\ y \end{pmatrix}\) = \(\begin{pmatrix}-1 \\ 8 \end{pmatrix}\)

  • A 3
  • B 4
  • C 7
  • D 12
jamb 1997mathematics

The correct answer is C. 7

\(\begin{pmatrix} 2 & -3 \\ -1 & 4 \end{pmatrix} \begin{pmatrix} x \\ y \end{pmatrix} = \begin{pmatrix} -1 \\ 8 \end{pmatrix}\)

\(\begin{pmatrix} 2x - 3y \\ -x + 4y \end{pmatrix} = \begin{pmatrix} -1 \\ 8 \end{pmatrix}\)

\(2x - 3y = -1 ... (i)\)

\(-x + 4y = 8 ... (ii)\)

From (ii), x = 4y - 8.

\(2(4y - 8) - 3y = -1 \implies 8y - 16 - 3y = -1\)

\(5y = -1 + 16 = 15 \implies y = 3\)

\(x = 4(3) - 8 = 12 - 8 = 4\)

\(\therefore x + y = 3 + 4 = 7\)

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