# How do you solve 5x + 3y = 46 and 2x + 5y = 7 using matrices?

Feb 15, 2017

Apply Gaussian Elimination/ Gauss-Jordan on an augmented matrix.

#### Explanation:

Convert the system into an augmented matrix like so: $\left[\begin{matrix}5 & 3 & 46 \\ 2 & 5 & 7\end{matrix}\right]$

Simplify to Reduced Row or Row Echelon form using elementary row operations:

Gaussian Elimination Example (REF):
$\left[\begin{matrix}1 & - 7 & 32 \\ 2 & 5 & 7\end{matrix}\right]$

$\left[\begin{matrix}1 & - 7 & 32 \\ 0 & 19 & - 57\end{matrix}\right]$

$\left[\begin{matrix}1 & - 7 & 32 \\ 0 & 1 & - \frac{57}{19}\end{matrix}\right]$

$\left[\begin{matrix}1 & - 7 & 32 \\ 0 & 1 & - 3\end{matrix}\right]$

So $1 x + - 7 y = 32$ and $y = - 3$
Thus $x = 32 + 7 \left(- 3\right) = 11$