Answer
$x = -3$, $y = 2$ or $(-3, 2)$
Work Step by Step
Given:
$5x - 2y = -19$
$2x + 3y = 0$
Multiply both sides of the first equation, $5x - 2y = -19$, by $3$:
$15x - 6y = -57$
Multiply both sides of the second equation, $2x + 3y = 0$, by $2$:
$4x + 6y = 0$
Add the first equation, $15x - 6y = -57$, to the second equation, $4x + 6y = 0$:
$15x - 6y + (4x + 6y) = -57 + (0)$
$15x + 4x - 6y + 6y = -57 + 0$
$19x = -57$
Divide both sides by $19$:
$x = -3$
Substitute $x = -3$ into the first equation, $5x - 2y = -19$:
$5x - 2y = -19$
$5(-3) - 2y = -19$
$-15 - 2y = -19$
Add $15$ to both sides:
$-2y = -4$
Divide both sides by $-2$:
$y = 2$
$x = -3$, $y = 2$
