How do you solve the system of equations 3x + 2y = - 7 and 2x - 7y = 37?

Apr 15, 2018

$x = 1$
$y = - 5$

Explanation:

$3 x + 2 y = - 7$ --- (1)
$2 x - 7 y = 37$ --- (2)

From (1),

$3 x + 2 y = - 7$
$3 x = - 2 y - 7$
$x = \frac{1}{3} \left(- 2 y - 7\right)$ --- (3)

Sub (3) into (2),

$2 \times \frac{1}{3} \left(- 2 y - 7\right) - 7 y = 37$

$\frac{2}{3} \left(- 2 y - 7\right) - 7 y = 37$

$- \frac{4}{3} y - \frac{14}{3} - 7 y = 37$

$- \frac{25}{3} y = \frac{125}{3}$

$y = - 5$ --- (4)

Sub (4) into (3),

$x = \frac{1}{3} \left(- 2 \left(- 5\right) - 7\right)$

$x = \frac{1}{3} \left(3\right)$

$x = 1$