[tex]\displaystyle\\
\left \{{{x+y=105}\atop{\dfrac{2}{3}x=\dfrac{1}{2}y}}\right.\\\\
\left\{{{x+y=105}\atop{\dfrac{2x}{3}-\dfrac{y}{2}=0}}\right.\\\\
\left\{{{x+y=105}\atop{\dfrac{4x}{6}-\dfrac{3y}{6}=0}~~\Big|\cdot 6} \right.\\\\\\
\left\{{{x+y=105~~|\cdot3}\atop{4x-3y=0}}\right.\\\\
\left\{{{3x+3y=315}\atop{4x-3y=0}}\right.\\
\text{- - - - - - - - - - -} \\
~~~~~7x~~/~~~=315\\\\
7x=315\\\\
x=\frac{315}{7}=\boxed{\bf45}\\
x+y=105\\
y=105-x=105-45=\boxed{\bf60}
[/tex]
