Question

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

Answer 1

y=
`(28)/(11)`
x=
`(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;

`(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]= (1)/(11) \left[\begin{array}{ccc}5&2\\-3&1\end{array}\right] \left[\begin{array}{ccc}2\\9\end{array}\right]`

Evaluating further;

`(1)/(11) \left[\begin{array}{ccc}11&0\\0&11\end{array}\right] \left[\begin{array}{ccc}x\\y\end{array}\right] = (1)/(11) \left[\begin{array}{ccc}28\\3\end{array}\right]`

x=
`(28)/(11) and y = (3)/(11)`