Answer
$x = \frac{20}{17}$, $y = \frac{19}{17}$ or $(\frac{20}{17}, \frac{19}{17})$
Work Step by Step
Given:
$2x - 3y = -1$
$3x + 4y = 8$
Multiply both sides of the first equation, $2x - 3y = -1$, by $3$:
$6x - 9y = -3$
Multiply both sides of the second equation, $3x + 4y = 8$, by $2$:
$6x + 8y = 16$
Subtract the first equation, $6x - 9y = -3$, from the second equation, $6x + 8y = 16$:
$6x + 8y - (6x - 9y) = 16 - (-3)$
$6x + 8y - (6x - 9y) = 19$
Subtract each term of the binomial:
$6x - 6x + 8y - (-9y) = 19$
$6x - 6x + 8y + 9y = 19$
$17y = 19$
Divide both sides by $17$:
$y = \frac{19}{17}$
Substitute $y = \frac{19}{17}$ into the first equation, $2x - 3y = -1$:
$2x - 3y = -1$
$2x - 3(\frac{19}{17}) = -1$
$2x - \frac{57}{17} = -1$
Add $\frac{57}{17}$ to both sides:
$2x = \frac{40}{17}$
Divide both sides by $2$:
$x = \frac{20}{17}$
$x = \frac{20}{17}$, $y = \frac{19}{17}$
