Answer
The capacity of the smaller truck is $4\;tons$
and the larger truck is $4\; tons$
Work Step by Step
Let the capacity of smaller truck is $x\;tons$.
And the capacity of larger truck is $y\;tons$.
$6$ trips of the smaller plus $3$ trips of the larger equal to $36\;tons$.
$\Rightarrow 6x+3y=36$ ...... (1)
$4$ trips of the smaller plus $8$ trips of the larger equal to $48\;tons$.
$\Rightarrow 4x+8y=48$ ...... (2)
Multiply equation (1) by $-2$.
$\Rightarrow -12x-6y=-72$ ...... (3)
Multiply equation (2) by $3$.
$\Rightarrow 12x+24y=144$ ...... (4)
Add equation (3) and equation (4).
$\Rightarrow -12x-6y+12x+24y=-72+144$
Simplify.
$\Rightarrow 18y=72$
Divide both sides by $18$.
$\Rightarrow y=4$.
Substitute the value of $y$ into equation (1).
$\Rightarrow 6x+3(4)=36$
Simplify.
$\Rightarrow 6x+12=36$
Isolate $x$.
$\Rightarrow x=\frac{36-12}{6}$
Simplify.
$\Rightarrow x=\frac{24}{6}$
$\Rightarrow x=4$.
Hence, the capacity of the smaller truck is $4\;tons$ and the larger truck is $4\; tons$.
