How do you solve the following system?: 9x +2y = 7 , -42x - 2y = -1

Jul 2, 2018

color(blue)(x = -2/11, y = 95/22

Explanation:

$9 x + 2 y = 7 , \text{ Eqn (1)}$

$- 42 x - 2 y = - 1. \text{ Eqn (2)}$

$\text{Adding Eqns (1) & (2)}$,

$9 x \cancel{+ 2 y} - 42 x \cancel{- 2 y} = 7 - 1$

$- 33 y = 6 \text{ or } x = - \frac{6}{33} = - \frac{2}{11}$

Substituting value of x in Eqn (1),

$\left(9 \cdot \left(- \frac{2}{11}\right)\right) + 2 y = 7$

$- 18 + 22 y = 77$

$y = \frac{77 + 18}{22} = \frac{95}{22}$