# How do you solve the system 3x - 2y = 10 and 5x + 3y = 4?

May 28, 2018

The solution is $\left\{\begin{matrix}x = 2 \\ y = - 2\end{matrix}\right.$

#### Explanation:

Solve the system of equations as follows :

$\left\{\begin{matrix}3 x - 2 y = 10. \ldots \ldots . \left(1\right) \\ 5 x + 3 y = 4. \ldots \ldots \ldots . \left(2\right)\end{matrix}\right.$

$3 \times$ Equation $\left(2\right) -$ $5 \times$Equation (1)

$\iff$ $\left\{\begin{matrix}3 x - 2 y = 10 \\ 0 + 19 y = - 38\end{matrix}\right.$

$\iff$ $\left\{\begin{matrix}3 x - 2 y = 10 \\ y = - 2\end{matrix}\right.$

$\iff$ $\left\{\begin{matrix}3 x - 2 \cdot - 2 = 10 \\ y = - 2\end{matrix}\right.$

$\iff$ $\left\{\begin{matrix}3 x = 10 - 4 \\ y = - 2\end{matrix}\right.$

$\iff$ $\left\{\begin{matrix}x = 2 \\ y = - 2\end{matrix}\right.$