Respuesta :
Let the weight (in kg) of a large box be 'x' and the weight of a small box be 'y'.
Given that the weight of 2 large boxes and 3 small boxes is 78 kg,
[tex]2x+3y=78[/tex]Also given that the weight of 6 large boxes and 5 small boxes is 180 kg,
[tex]6x+5y=180[/tex]Here we will apply the Elimination Method to solve both the equations.
Consider the three times the first equation being subtracted from the second equation,
[tex](6x+5y)-3(2x+3y)=180-3(78)\Rightarrow6x+5y-6x-9y=180-234[/tex]Simplify the terms,
[tex]-4y=-54\Rightarrow y=\frac{54}{4}=13.5[/tex]Substitute this value in the first equation,
[tex]2x+3(13.5)=78\Rightarrow2x=78-40.5\Rightarrow2x=37.5\Rightarrow x=18.75[/tex]Thus, the larger box weighs 18.75 kg while the small box weighs 13.5 kg
