Let the weight of a large box be x .
Let the weight of a small box be y .
According to the first condition,
[tex]5x\text{ + 3y = 120 \_\_\_\_\_\_\_(1)}[/tex]According to the second condition,
[tex]7x\text{ }+\text{ 9y = 234\_\_\_\_\_\_\_(2)}[/tex]Multiplying equation ( 1 ) by 3 ,
[tex]15x\text{ + 9y =360 \_\_\_\_\_\_(3)}[/tex]Subtracting equation (2) from (3),
[tex]\begin{gathered} 8x\text{ = 126} \\ x\text{ = }\frac{126}{8} \\ x\text{ = 15.75} \end{gathered}[/tex]Substituting the value of x = 15.75 in equation ( 1 ),
[tex]\begin{gathered} 5(15.75)\text{ + 3y = 120} \\ 78.75\text{ + 3y = 120} \\ 3y\text{ = 120 - 78.75} \end{gathered}[/tex]Further,
[tex]\begin{gathered} 3y\text{ = 41.25} \\ y\text{ = }\frac{41.25}{3} \\ y\text{ = 13.75} \end{gathered}[/tex]Thus the weight of a larger box is 15.75 kilograms and weight of a smalller box is 13.75 kilograms.
