Let's take lemonade's price as 'x' and iced tea's price as 'y'.
[tex] \left \{ {{3x+4y=12} \atop {5x+2y=11.5}} \right.
\\ \left \{ {{x=4-y} \atop {5(4-y)+2y=11.5}} \right.
\\ \left \{ {{x=4-y} \atop {20-3y=11.5}} \right.
\\ \left \{ {{x=4-y} \atop {y=2.83}} \right.
\\ \left \{ {{x=1.17} \atop {y=2.83}} \right. [/tex]
Price of lemonade is $2.83, iced tea's $1.17.
