Lets define the variables
x - burger
y - hotdogs
Now lets write our equation
2x+5y=12.75
3x+2y=12.25
Now we solve by subsitution or elimination.
2x+5y=12.75
0.4x+y=2.55
y=-0.4x+2.55
3x+2(-0.4x+2.55)=12.25
3x-0.8x+5.1=12.25
2.2x=7.15
x=3.25
Plug in X
3(3.25)+2y=12.25
9.75+2y=12.25
2y=2.5
y=1.25
Your final answer is 3.25, 1.25
Plug it in to check!