How do you solve this system of equations: 3x + y = 6; 5x + 4y = 10?

Jun 7, 2018

$\left(2 , 0\right)$

Explanation:

No mercy.

$\left(\begin{matrix}3 & 1 \\ 5 & 4\end{matrix}\right) \left(\begin{matrix}x \\ y\end{matrix}\right) = \left(\begin{matrix}6 \\ 10\end{matrix}\right)$

$D = \det \left[3 , 5 , 1 , 4\right] = 3 \cdot 4 - 5 \cdot 1 = 7$

$x = \frac{\det \left[6 , 10 , 1 , 4\right]}{D} = \frac{6 \cdot 4 - 10 \cdot 1}{7} = 2$

$y = \frac{\det \left[3 , 5 , 6 , 10\right]}{D} = \frac{3 \cdot 10 - 5 \cdot 6}{7} = 0$