How do you solve the following system?: -x -2y =-1, 6x -y = -4

Jan 18, 2016

$x = \frac{7}{13}$ and $y = \frac{10}{13}$

Explanation:

By Cramer's rule:

Make a matrix with the coefficient of each columns, in this case

$\left[\begin{matrix}- 1 & - 2 \\ 6 & - 1\end{matrix}\right]$

Take the determinant of this

$| \left(- 1 , - 2\right) , \left(6 , - 1\right) | = 13$

Now replace the first row with the results row

$\left[\begin{matrix}- 1 & - 2 \\ - 4 & - 1\end{matrix}\right]$

Now take this determinant

$| \left(- 1 , - 2\right) , \left(- 4 , - 1\right) | = 7$

The ratio of these determinants is the solution for $x$, so

$x = \frac{7}{13}$

Replace the $y$ row by the results row

$\left[\begin{matrix}- 1 & - 1 \\ 6 & - 4\end{matrix}\right]$

Take this determinant

$| \left(- 1 , - 1\right) , \left(6 , - 4\right) | = 10$

Like before the ratio is the answer for $y$

$y = \frac{10}{13}$