How do you solve the following system?: y=2x + 3 , 9y = -3x - 9

May 25, 2016

The solution for the system of equations is:
color(blue)(x = -12/7

color(blue)(y = -3/7

Explanation:

color(blue)(y = 2x +3 ..............equation $\left(1\right)$
$9 y = - 3 x - 9$....equation $\left(2\right)$

Substituting equation $1$ in equation $2 :$

$9 y = - 3 x - 9$

$9 \times \left(\textcolor{b l u e}{2 x + 3}\right) = - 3 x - 9$

$18 x + 27 = - 3 x - 9$

$18 x + 3 x = - 9 - 27$

$21 x = - 36$

$x = - \frac{36}{21}$

color(blue)(x = -12/7

Finding $y$ from equation $\left(1\right) :$
$y = 2 x + 3$

$y = 2 \times \left(- \frac{12}{7}\right) + 3$

$y = - \frac{24}{7} + 3$

$y = - \frac{24}{7} + \frac{21}{7}$

color(blue)(y = -3/7