# How do solve the following linear system?:  3x – 2y = 7 , 11x + 3y + 7 = 0 ?

Dec 28, 2015

$3 x - 2 y = 7. \ldots \ldots \ldots \left(i\right)$
$11 x + 3 y + 7 = 0 \implies 11 x + 3 y = - 7. \ldots \ldots \ldots . . \left(i i\right)$
Multiply $\left(i\right)$ by $3$ and (ii) by 2 and add
$\implies 9 x - 6 y = 21$
$22 x + 6 y = - 14$

$31 x + 0 = 7$

$\implies x = \frac{7}{31}$

Put $x = \frac{7}{31}$ in $\left(i\right)$

$\implies 3 \left(\frac{7}{31}\right) - 2 y = 7$

$\implies \frac{21}{31} - 2 y = 7$

$\implies 2 y = \frac{21}{31} - 7$

$\implies 2 y = \frac{21 - 217}{31}$

$\implies 2 y = - \frac{196}{31}$

$\implies y = - \frac{98}{31}$