Question

The senior classes at High School A and High School B planned separate trips to the indoor climbing gym. The senio class at High School A rented and filled 2 vans and 2 buses with 106 High School B rented and filled 8 vans and i bus with 151 students. Each van and students. each bus carried the same number of students. How many students can a van carry? How many students can a bus carry?

Answer 1

Let x person in 1 van and y persons in 1 bus
 so for school  A  took    2x+2y=106
for school  B  took    8x+y=151

make a system
$\left \{ {{2x+2y=106} \atop {8x+y=151}} \right.$
solve it:
multiply second equation by 2
2*8x+2*y=2*151
16x+2y=302

second equation minus first we have:
16x+2y-2x-2y=302-106
14x=196
x=14 - persons in 1 van

to find y put x=14 in equation:
2x+2y=106
2*14+2y=106
2y=106-28
2y=78
y=39
Answer:  1 van can carry 14persons, 1 bus can carry 39 persons