Answer
($-\frac{17}{2}, -\frac{3}{2}$)
Work Step by Step
1. Multiply each equation by its LCD.
3($-\frac{x}{3} + y) = 3(\frac{4}{3})$
2($\frac{x}{2} - \frac{5}{2}y) = 2(-\frac{1}{2})$
Simplifies to:
-x + 3y = 4
x - 5y = -1
2. Add the equations and solve for y:
-2y = 3
y = $-\frac{3}{2}$
3. Let y = $-\frac{3}{2}$ in the first equation to find x:
$-\frac{x}{3} + (-\frac{3}{2}) = \frac{4}{3}$
$-\frac{x}{3} = \frac{4}{3} + \frac{3}{2}$
$-\frac{x}{3} = \frac{17}{6}$
x = $-\frac{17}{2}$
4. Check the solution ($-\frac{17}{2}, -\frac{3}{2}$) in the second equation:
$\frac{-\frac{17}{2}}{2} - \frac{5}{2}(-\frac{3}{2}) = -\frac{1}{2}$
$\frac{-17}{4} + \frac{15}{4} = -\frac{1}{2}$
$-\frac{2}{4} = -\frac{1}{2}$
$ -\frac{1}{2} = -\frac{1}{2}$
True
