[tex]x-the\ cost\ of\ a\ hamburger\\y-the\ cost\ of\ a\ medium\ friest\\z-the\ cost\ of\ a\ medium\ drink\\\\ \left\{\begin{array}{ccc}4x+3y=17.35\\x+y+z=6.09&\to z=6.09-x-y\\2x+y+z=9.34\end{array}\right\\ \left\{\begin{array}{ccc}4x+3y=17.35\\2x+y+6.09-x-y=9.34\end{array}\right\\\left\{\begin{array}{ccc}4x+3y=17.35\\x=9.34-6.09\end{array}\right\\\left\{\begin{array}{ccc}4x+3y=17.35\\x=3.25\end{array}\right[/tex]
[tex]\left\{\begin{array}{ccc}4\cdot11.26+3y=17.35\\x=3.25\end{array}\right\\\left\{\begin{array}{ccc}4\cdot3.25+3y=17.35\\x=3.25\end{array}\right\\\left\{\begin{array}{ccc}13+3y=17.35\\x=3.25\end{array}\right\\\left\{\begin{array}{ccc}3y=17.35-13\\x=3.25\end{array}\right\\\left\{\begin{array}{ccc}3y=4.35\\x=3.25\end{array}\right\\\left\{\begin{array}{ccc}y=1.45\\x=3.25\end{array}\right\\[/tex]
[tex]\left\{\begin{array}{ccc}x=3.25\\y=1.45\\z=6.09-3.25-1.45\end{array}\right\\\left\{\begin{array}{ccc}x=3.25\\y=1.45\\z=1.39\end{array}\right\\\\\\Answer:\\Hamburger-\$3.25\\Medium\ fries-\$1.45\\Medium\ drink:\$1.39[/tex]