Question #236240

Using matrix method, solve the simultaneous equations {x-3y=3

5x-9y=11


1
Expert's answer
2021-09-20T17:34:28-0400

Axˉ=bˉA\bar x=\bar b

A=(1359),bˉ=(311)A=\begin{pmatrix} 1 & -3 \\ 5 & -9 \end{pmatrix},\bar b=\begin{pmatrix} 3 \\ 11 \end{pmatrix} .

det(A)=9+15=6.det(A)=-9+15=6.

A1=16(9351)A^{-1}=\frac{1}{6}\begin{pmatrix} -9 & 3 \\ -5 & 1 \end{pmatrix}

xˉ=(xy)=A1bˉ=16(9351)(311)=16(64)=(123)\bar x=\begin{pmatrix} x \\ y \end{pmatrix}=A^{-1}\bar b=\frac{1}{6}\begin{pmatrix} -9& 3 \\ -5 & 1 \end{pmatrix}\begin{pmatrix} 3 \\ 11 \end{pmatrix}=\frac{1}{6}\begin{pmatrix} 6 \\ -4 \end{pmatrix}=\begin{pmatrix} 1 \\ -\frac{2}{3} \end{pmatrix}

Thus, x=1,y=23.x=1,y=-\frac{2}{3}.



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