Answer:
small box = 6kg
large box = 18.5kg
Step-by-step explanation:
8 large + 3 small = 166kg
2 large + 5 small = 67kg
Our equations are:
[tex]8l+3s=166\\2l+5s=67[/tex]
Multiply by -4 the second equation to make l eliminable.
[tex](-4)(2l+5s=67)\\-8l-20s=-268[/tex]
Now add both equations.
[tex]8l+3s=166\\-8l-20s=-268\\[/tex]
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[tex]-17s=-102[/tex]
Solve for s;
[tex]s=\frac{-102}{-17}\\s= 6[/tex]
Now replace the value of s in any of your main equations to find l.
[tex]8l+3s=166\\8l+3(6)=166\\8l+18=166\\8l=166-18\\8l=148\\l=\frac{148}{8}\\ l=18.5[/tex]
Now replace both l and s in the equations to find if they're the real values that satisfy the equation.
[tex]8(18.5)+3(6)=166\\148+18=166\\166=166[/tex]
[tex]2l+5s=67\\2(18.5)+5(6)=67\\37+30=67\\67=67[/tex]
Therefore we can conclude that these are the real values that satisfy the equations.
