# How do you solve the following system: x-2y=3, 2x+3y =4 ?

Feb 22, 2016

The solution for the system of equations is:

$x = \frac{17}{7}$
$y = - \frac{2}{7}$

#### Explanation:

$x - 2 y = 3$ , multiplying by $2$
$\textcolor{b l u e}{2 x} - 4 y = 6$.......equation $\left(1\right)$

$\textcolor{b l u e}{2 x} + 3 y = 4$........equation $\left(2\right)$

Solving by elimination:

subtracting equation $2$ from $1$:

$\cancel{\textcolor{b l u e}{2 x}} - 4 y = 6$

$- \cancel{\textcolor{b l u e}{2 x}} - 3 y = - 4$

$- 7 y = 2$

$y = - \frac{2}{7}$

Finding $x$ from equation $1$:
$x - 2 y = 3$

$x = 3 + 2 y$

$x = 3 + 2 \times \left(- \frac{2}{7}\right)$

$x = 3 - \frac{4}{7}$

$x = \frac{21}{7} - \frac{4}{7}$

$x = \frac{17}{7}$