# How do you solve 3x + 4y = 24  and 6x - 1y = 21 using matrices?

Aug 30, 2016

$x = 4 , y = 3$

#### Explanation:

First let's build the matrix by filling its rows by the coefficients of the system in its standard form:

$D = \left(\begin{matrix}3 & 4 \\ 6 & - 1\end{matrix}\right) = 3 \left(- 1\right) - 4 \left(6\right) = - 3 - 24 = - 27$

Then you build the matrices ${D}_{x}$ and ${D}_{y}$ by substituting the known terms in the first and the second column, respectively:

${D}_{x} = \left(\begin{matrix}24 & 4 \\ 21 & - 1\end{matrix}\right) = 24 \left(- 1\right) - 4 \left(21\right) = - 24 - 84 = - 108$

${D}_{y} = \left(\begin{matrix}3 & 6 \\ 24 & 21\end{matrix}\right) = 3 \left(21\right) - 6 \left(24\right) = 63 - 144 = - 81$

Then you can solve by calculating:

$x = \frac{{D}_{x}}{D} = \frac{- 108}{- 27} = 4$

$y = \frac{{D}_{y}}{D} = \frac{- 81}{- 27} = 3$