By applying inverse of a matrix, we find that the solution of the system of <em>linear</em> equations is (x, y) = (5/7, - 2/7).
<h3>How to solve a system of equation with inverse matrices</h3>
In linear algebra, systems of <em>linear</em> equations with a unique solution can be represented by the following expression:
(1)
Where:
- Matrix of dependent constants.
- Vector column of variables.
- Vector column of independent constants.
The solution of such systems is defined by:

, where
.
Where:
- Determinant of the matrix of dependent constants.
- Adjoint of the matrix of dependent constants.
For the case of
, the inverse of
is:
(2)
If we know that
and
, then the solution of the system of linear equations is:
![\vec A^{-1}= \frac{1}{(3)\cdot (2) - (5) \cdot (4)}\cdot \left[\begin{array}{cc}2&-4\\-5&3\end{array}\right]](https://tex.z-dn.net/?f=%5Cvec%20A%5E%7B-1%7D%3D%20%5Cfrac%7B1%7D%7B%283%29%5Ccdot%20%282%29%20-%20%285%29%20%5Ccdot%20%284%29%7D%5Ccdot%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D2%26-4%5C%5C-5%263%5Cend%7Barray%7D%5Cright%5D)
![\vec A^{-1} = -\frac{1}{14}\cdot \left[\begin{array}{cc}2&-4\\-5&3\end{array}\right]](https://tex.z-dn.net/?f=%5Cvec%20A%5E%7B-1%7D%20%3D%20-%5Cfrac%7B1%7D%7B14%7D%5Ccdot%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D2%26-4%5C%5C-5%263%5Cend%7Barray%7D%5Cright%5D)
![\vec A^{-1} = \left[\begin{array}{cc}-\frac{1}{7} &\frac{2}{7} \\\frac{5}{14} &-\frac{3}{14} \end{array}\right]](https://tex.z-dn.net/?f=%5Cvec%20A%5E%7B-1%7D%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D-%5Cfrac%7B1%7D%7B7%7D%20%26%5Cfrac%7B2%7D%7B7%7D%20%5C%5C%5Cfrac%7B5%7D%7B14%7D%20%26-%5Cfrac%7B3%7D%7B14%7D%20%5Cend%7Barray%7D%5Cright%5D)
![\vec x = \left[\begin{array}{cc}-\frac{1}{7} &\frac{2}{7} \\\frac{5}{14} &-\frac{3}{14} \end{array}\right] \cdot \left[\begin{array}{cc}1\\3\end{array}\right]](https://tex.z-dn.net/?f=%5Cvec%20x%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D-%5Cfrac%7B1%7D%7B7%7D%20%26%5Cfrac%7B2%7D%7B7%7D%20%5C%5C%5Cfrac%7B5%7D%7B14%7D%20%26-%5Cfrac%7B3%7D%7B14%7D%20%5Cend%7Barray%7D%5Cright%5D%20%5Ccdot%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1%5C%5C3%5Cend%7Barray%7D%5Cright%5D)
![\vec x = \left[\begin{array}{cc}\frac{5}{7} \\-\frac{2}{7} \end{array}\right]](https://tex.z-dn.net/?f=%5Cvec%20x%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%5Cfrac%7B5%7D%7B7%7D%20%5C%5C-%5Cfrac%7B2%7D%7B7%7D%20%5Cend%7Barray%7D%5Cright%5D)
By applying inverse of a matrix, we find that the solution of the system of <em>linear</em> equations is (x, y) = (5/7, - 2/7).
To learn more on inverse of matrices: brainly.com/question/4017205
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