Question

Solve the system using a matrix.
(8x + 5y = 38
(3x + 2y = 14
([ ? ],[_])

Answer 1

(x, y) = (6, -2)

Explanation:

A suitable calculator or spreadsheet can do the row-reduction or matrix inversion required to solve this system.

(x, y) = (6, -2)

_____

For matrices ...

`A=\left[\begin{array}{cc}8&5\\3&2\end{array}\right],\ B=\left[\begin{array}{c}38\\14\end{array}\right] ,\ X=\left[\begin{array}{c}x\\y\end{array}\right]`

The solution can be found as ...

`AX=B\ \longrightarrow\ X=A^(-1)B`

or by row-reducing the augmented matrix ...

`[A|B]\ \longrightarrow\ [I|X]`