Question

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

Answer 1

Answer:

  (x, y) = (6, -2)

Step-by-step 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 ...

  $[A|B]\ \longrightarrow\ [I|X]$