Answer
$x=12$ and $y=6$
Work Step by Step
We need to solve the given system of equations:
$\dfrac{1}{3}x - \dfrac{3}{2}y = -5 ...(1)$
and $\dfrac{3}{4}x + \dfrac{1}{3}y=11 ....(2)$
We need to multiply equation (1) by $\dfrac{1}{3}$ and equation (2) by $\dfrac{3}{2}$
$\dfrac{1}{9}x - \dfrac{1}{2}y = -\dfrac{5}{3} ... (3)$
$\dfrac{9}{8}x + \dfrac{1}{2}y = \dfrac{33}{2} ...(4)$
Now, we will add equations (3) and (4).
$(\dfrac{1}{9} + \dfrac{9}{8})x = -\dfrac{5}{3} + \dfrac{33}{2}
\\ \dfrac{89}{72}x = \dfrac{89}{6} \\ x=12$
Finally, back substitute into equation (2).
$\dfrac{1}{3}y = 11 - \dfrac{3}{4}(12) \\ \implies y=6$
Thus, the solutions to the two given equations are:
$x=12$ and $y=6$
