Question

Solve for x and y:

$\frac{3x}{2}-\frac{5y}{3}+2=0$
$\frac{x}{3}+\frac{y}{2}=2\frac{1}{6}$

Answer 1

$\left(\frac{3x}{2}\right)-\left(\frac{5y}{3}\right)+2=0\to \left(1.\right)\left(\frac{x}{3}\right)+\left(\frac{y}{2}\right)=\left(\frac{13}{16}\right)\to \left(2.\right)multiplyequation\left(1\right)by\left(\frac{2}{9}\right),weget\left(\frac{x}{3}\right)-\left(\frac{10y}{27}\right)+\left(\frac{4}{9}\right)=0\to \left(1.\right)nowsubtracte{q}^n\left(1\right)-\left(2\right),weget\left(\frac{-10y}{27}\right)-\left(\frac{y}{2}\right)+\left(\frac{4}{9}\right)-\left(\frac{13}{6}\right)=0\left(\frac{8-39}{18}\right)=\left(\frac{20y+27y}{54}\right)\left(\frac{-31}{18}\right)=\left(\frac{47y}{54}\right)\therefore y=\left(\frac{-31\times 3}{47}\right)=\left(\frac{-93}{47}\right)\therefore x=\left(\right(\frac{13}{6})-(\frac{y}{2}\left)\right)\times 3=\left(\right(\frac{13}{6})+(\frac{93}{94}\left)\right)\times =\left(\frac{(1222+558)\times 3}{6\times 94}\right)=\left(\frac{890}{94}\right)=\left(\frac{445}{47}\right)$