Mathematics: Solve the system of equations; x - 2y = 2 and 3x - 5y = 9 by writing and solving a matrix equation. show all your work.

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Solve the system of equations; x - 2y = 2 and

Ответ:

Fredo10

01.01.2022

Y= $\frac{28}{11}$
x= $\frac{3}{11}$

Working;
Start by forming a matrix as shown below;
$\left[\begin{array}{ccc}1&-2\\3&5\end{array}\right] ( \left[\begin{array}{ccc}x\\y\end{array}\right])= ( \left[\begin{array}{ccc}2\\9\end{array}\right])$

Step II
Finding the inverse of the matrix as shown below;
Determinant;
(1*5)-(3*(-2)=11
Inverse;
$\frac{1}{11} \left[\begin{array}{ccc}5&2\\-3&1\end{array}\right] \left[\begin{array}{ccc}1&-2\\3&5\end{array}\right] \left[\begin{array}{ccc}x\\y\end{array}\right]= \frac{1}{11} \left[\begin{array}{ccc}5&2\\-3&1\end{array}\right] \left[\begin{array}{ccc}2\\9\end{array}\right]$

Evaluating further;
$\frac{1}{11} \left[\begin{array}{ccc}11&0\\0&11\end{array}\right] \left[\begin{array}{ccc}x\\y\end{array}\right] = \frac{1}{11} \left[\begin{array}{ccc}28\\3\end{array}\right]$

x= $\frac{28}{11} and y = \frac{3}{11}$

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Solve the system of equations; x - 2y = 2 and 3x - 5y = 9 by writing and solving a matrix equation. show all your work.

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