Answer to Question #275758 in Algebra for Rohosafi

Question

Solve 7x+9y=3

5x+7y=1 using matrix method

Answer 1

7x+9y=3

5x+7y=1

write the equation in matrix notation

$\begin{bmatrix} 7 & 9 \\ 5 & 7 \end{bmatrix}$ * $\begin{bmatrix} x \\ y \end{bmatrix}$ =$\begin{bmatrix} 3 \\ 1 \end{bmatrix}$

$X=A^{-1}B$

where $X=\begin{bmatrix} x \\ y \end{bmatrix}$

$A^{-1}=\frac{1}{det}\begin{bmatrix} 7 & -9 \\ -5 & 7 \end{bmatrix}$

$B=\begin{bmatrix} 3 \\ 1 \end{bmatrix}$

det=(7*7)-(5*9)

=4

$\begin{bmatrix} x\\ y \end{bmatrix}=\frac 1 4*\begin{bmatrix} 7& -9\\ -5 & 7 \end{bmatrix}* \begin{bmatrix} 3 \\ 1 \end{bmatrix}$

$\begin{bmatrix} x\\ y \end{bmatrix}=\frac 1 4*\begin{bmatrix} 12\\ -8 \end{bmatrix}$

$\begin{bmatrix} x\\ y \end{bmatrix}=\begin{bmatrix} 3\\ -2 \end{bmatrix}$

x=3 and y=-2