# How do solve the following linear system?:  2x +5y - 21 = 0 , 3x – 2y = 7 ?

Feb 27, 2016

$2 x + 5 y - 21 = 0 - - - - - - - \left(1\right)$
$3 x - 2 y - 7 = 0 - - - - - - - \left(2\right)$
By cross multiplication we have
$\frac{x}{5 \cdot \left(- 7\right) - \left(- 2\right) \cdot \left(- 21\right)} = \frac{y}{- 21 \cdot 3 - \left(- 7\right) \cdot 2}$

$= \frac{1}{2 \cdot \left(- 2\right) - 5 \cdot 3}$

$\implies x = \frac{77}{19}$

$\implies y = \frac{49}{19}$