This season, Lisa's lacrosse team has won 2/3 of their home games (games played at Lisa's school), but just 2/5 of their away game

Let X be the at home games and Y be the away games

then

X+Y=49     (1)         

and

$$\\\frac{2X}{3}+\frac{2Y}{5}=26\\\\ 15\left(\frac{2X}{3}+\frac{2Y}{5}\right)=15*26\\\\ \frac{15*2X}{3}+\frac{15*2Y}{5}=15*26\\\\ 10X+6Y=390\\\\ 5X+3Y=195\qquad(2)\\\\$$

3X+3Y=147        3*(1)          (1b)

(2)-(1b)

2X=48

X=24

X+Y=49

24+Y=49

Y=49-24

y=25

24 home games      25 away games.