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JAMB Mathematics 2014 Paper

Question : 20

Total: 47

Find y, if

\begin{pmatrix} 5 & -6 \\ 2 & -7 \end{pmatrix}\begin{pmatrix} x \\ y \end{pmatrix} = \begin{pmatrix} 7 \\ -11 \end{pmatrix}

Solution:

Concept:

Matrix multiplication gives a system of linear equations. Solve for

y

using elimination.

Explanation:

Multiply the matrices to form two equations.

5x - 6y = 7 \quad ...(1)

2x - 7y = -11 \quad ...(2)

Eliminate

x

by making its coefficients equal.

Multiply (1) by 2:

10x - 12y = 14 \quad ...(3)

Multiply (2) by 5:

10x - 35y = -55 \quad ...(4)

Subtract (4) from (3):

(10x - 12y) - (10x - 35y) = 14 - (-55)

23y = 69

y = \frac{69}{23} = 3

Answer:

y = 3

, so the correct option is C.

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