# How would you solve the system of these two linear equations: 2x + 3y = -1 and x - 2y = 3? Enter your solution as an ordered pair (x,y).

Nov 22, 2015

$\left(1 , - 1\right)$

#### Explanation:

Given,

$\left\{\begin{matrix}2 x + 3 y = - 1 \textcolor{w h i t e}{\times \times \times} \text{---(I)" \\ x - 2y = 3 color(white)(xxxxxxxxx) "---(II)}\end{matrix}\right.$

Multiply $\text{(II)}$ by $2$ and then subtract from $\text{(I)}$,

$7 y = - 7$
$\textcolor{w h i t e}{x} y = - 1$

Putting $y = - 1$ in $\text{(I)}$,

$2 x + 3 \left(- 1\right) = - 1$

$\textcolor{w h i t e}{\times \times \times x} 2 x = - 1 + 3$

$\textcolor{w h i t e}{\times \times \times x} 2 x = 2$

$\textcolor{w h i t e}{\times \times \times \times} x = 1$.

Hence, $x = 1$ and $y = - 1$