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From the condition, you get these two equations
10*V + 7*B = 341 students (1) (V = is the van capacity; B = the bus capacity)
5V + 8*B = 319 students (2)
Multiply eq(2) by 2 (both sides). Keep eq(1) as is. You will get an EQUIVALENT system
10*V + 7*B = 341 (1')
10V + 16*B = 638 (2')
Now subtract eq(1') from eq(2'). The terms "10V" will cancel each other, and you will get a single equation for one unknown B:
16B - 7B = 638 - 341
9B = 297 =============> B = 297/9 = 33.
Now from eq(1), V = = 11.
Answer. The bus capacity is 33 students. The van capacity is 11 students.
Solved.
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In the solution, I used the Elimination method to solve the system.
So, on the way, you learned on how the Elimination method works.