# How do you solve the system 3x+2y=19 and 2x-3y=-9 by substitution?

May 24, 2015

$3 x + 2 y = 19 \to 3 x = 19 - 2 y \to x = \frac{19 - 2 y}{3}$

$2 x - 3 y = - 9 \to \left(\frac{2}{3}\right) . \left(19 - 2 y\right) - 3 y = - 9$

$38 - 4 y - 9 y = - 27 \to - 13 y = - 27 - 38 = - 65$

$y = \frac{65}{13}$ = 5

$x = \frac{19 - 10}{3} = \frac{9}{3} = 3$

Check: 3(3) + 2(5) = 19. OK