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  • Solve system of linear equations, using matrix method.4x - 3y = 3 , 3x - 5y = 7.

Q : 9       Solve system of linear equations, using matrix method.

               \small 4x-3y=3

               \small 3x-5y=7

Answers (1)

best_answer

The given system of equations

\small 4x-3y=3

\small 3x-5y=7

can be written in the matrix form of AX =B, where

A = \begin{bmatrix} 4 &-3 \\ 3& -5 \end{bmatrix}, X = \begin{bmatrix} x\\y \end{bmatrix}  and B = \begin{bmatrix} 3\\7 \end{bmatrix}

we have, 

|A| = -20+9=-11 \neq 0.

So, A is non-singular, Therefore, its inverse A^{-1} exists.

as we know A^{-1} = \frac{1}{|A|} (adjA)

A^{-1} = \frac{1}{|A|} (adjA) = \frac{-1}{11}\begin{bmatrix} -5 &3 \\ -3& 4 \end{bmatrix} = \frac{1}{11} \begin{bmatrix} 5 &-3 \\ 3& -4 \end{bmatrix}

So, the solutions can be found by X = A^{-1}B = \frac{1}{11}\begin{bmatrix} 5 &-3 \\ 3 & -4 \end{bmatrix}\begin{bmatrix} 3\\7 \end{bmatrix}

\Rightarrow \begin{bmatrix} x\\y \end{bmatrix} = \frac{1}{11}\begin{bmatrix} 15-21\\ 9-28 \end{bmatrix} = \frac{1}{11}\begin{bmatrix} -6\\-19 \end{bmatrix}= \begin{bmatrix} -\frac{6}{11}\\ \\-\frac{19}{11} \end{bmatrix}

Hence the solutions of the given system of equations;

x =\frac{-6}{11} \ and\ y =\frac{-19}{11}.

Posted by

Divya Prakash Singh

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