# How do you solve the following system: -2x + 5y = 20, 2x +5y = 5 ?

Feb 27, 2016

$- 2 x + 5 y = 20 - - - - - \left(1\right)$
$2 x + 5 y = 5 - - - - - - \left(2\right)$
By adding eqn (1) and eqn(2) we get
$- \cancel{2} x + 5 y + \cancel{2} x + 5 y = 20 + 5$
$\implies 10 y = 25$
$\implies y = \frac{25}{10} = \frac{5}{2}$
putting the value of y in eqn(2)
$2 x + 5 \cdot \frac{5}{2} = 5$
$\implies 2 x = 5 - \frac{25}{2} = - \frac{15}{2}$
$\implies x = - \frac{15}{4} = - 3 \frac{3}{4}$