Mathematics 2019 JAMB Past Questions - Question 17: Solve for x and y (1 1) (x) = (4) (3 y) (1) (1)

Correct Answer

C

Explanation

The given equation is a matrix equation. To solve for \( x \) and \( y \), we can use matrix multiplication.The equation can be written as:\[ \begin{pmatrix} 1 & 1 \\ 3 & 1 \end{pmatrix} \begin{pmatrix} x \\ y \end{pmatrix} = \begin{pmatrix} 4 \\ 3 \end{pmatrix} \]To solve for \( x \) and \( y \), we can multiply the inverse of the left-hand matrix by the right-hand matrix.The inverse of the matrix \( \begin{pmatrix} 1 & 1 \\ 3 & 1 \end{pmatrix} \) is:\[ \frac{1}{(1)(1) - (1)(3)} \begin{pmatrix} 1 & -1 \\ -3 & 1 \end{pmatrix} = \frac{1}{-2} \begin{pmatrix} 1 & -1 \\ -3 & 1 \end{pmatrix} = \begin{pmatrix} -\frac{1}{2} & \frac{1}{2} \\ \frac{3}{2} & -\frac{1}{2} \end{pmatrix} \]Now, we can multiply the inverse by the right-hand matrix:\[ \begin{pmatrix} -\frac{1}{2} & \frac{1}{2} \\ \frac{3}{2} & -\frac{1}{2} \end{pmatrix} \begin{pmatrix} 4 \\ 3 \end{pmatrix} = \begin{pmatrix} -\frac{1}{2}(4) + \frac{1}{2}(3) \\ \frac{3}{2}(4) - \frac{1}{2}(3) \end{pmatrix} = \begin{pmatrix} -2 + \frac{3}{2} \\ 6 - \frac{3}{2} \end{pmatrix} = \begin{pmatrix} -\frac{1}{2} \\ \frac{9}{2} \end{pmatrix} \]So, the solution is \( x = -\frac{1}{2} \) and \( y = \frac{9}{2} \).Therefore, the correct answer is not among the options provided.