Solve the system. 2/3 x - 1 /2 y = 1 1/ 4 x + 3/8 y = -1 A) (3, 2) B) (9, 10) C) ( 9/ 2 , 5) D) (- 1 /3 , - 22 /9 )

Answer:[tex]\large\boxed{D)\ \left(-\dfrac{1}{3},\ -\dfrac{22}{9}\right)}[/tex]Step-by-step explanation:[tex]\left\{\begin{array}{ccc}\dfrac{2}{3}x-\dfrac{1}{2}y=1&\text{multiply both sides by 6}\\\dfrac{1}{4}x+\dfrac{3}{8}y=-1&\text{multiply both sides by 8}\end{array}\right\\\left\{\begin{array}{ccc}6\!\!\!\!\diagup^2\cdot\dfrac{2}{3\!\!\!\!\diagup_1}x-6\!\!\!\!\diagup^3\cdot\dfrac{1}{2\!\!\!\!\diagup_1}y=6\cdot1\\8\!\!\!\!\diagup^2\cdot\dfrac{1}{4\!\!\!\!\diagup_1}x+8\!\!\!\!\diagup^1\cdot\dfrac{3}{8\!\!\!\!\diagup_1}y=8\cdot(-1)\end{array}\right[/tex][tex]\underline{+\left\{\begin{array}{ccc}4x-3y=6\\2x+3y=-8\end{array}\right}\qquad\text{add both saides of the equations}\\.\qquad6x=-2\qquad\text{divide both sides by 6}\\.\qquad x=-\dfrac{2}{6}\\\\.\qquad\boxed{x=-\dfrac{1}{3}}\\\\\text{Put the value of x to the second equation:}\\\\2\left(-\dfrac{1}{3}\right)+3y=-8\\\\-\dfrac{2}{3}+3y=-8\qquad\text{add}\ \dfrac{2}{3}\ \text{to both sides}\\\\3y=-\dfrac{24}{3}+\dfrac{2}{3}[/tex][tex]3y=-\dfrac{22}{3}\qquad\text{divide both sides by 3}\ /multiply\ both\ sides\ by\ \frac{1}{3}/\\\\\boxed{y=-\dfrac{22}{9}}[/tex]