Oni's school went on a field trip to the zoo. They took 3 buses and 2 vans for a total of 118 students. On another trip they took 1 bus and 7 vans to transport 128 students. How many students rode each van and each bus?

X = bus Y = van

3x+2y=118

X+7y=128

Multiply the bottom row by - 3

3x+2y=118

-3x-21y = - 384

-19y=-266

Y=14. 3x+2 (14) = 118

3x+28=118

3x = 90

X=30

14 students rode in a van and 30 rode in a bus.

Step-by-step explanation:

Let the number of students who rode on a van = v and the number on a bus be b.

Then we have the system of equations:

3b + 2v = 118

b + 7v = 128

Multiply the second equation by 3:-

3b + 21v = 384

3b + 2v = 118 Subtract:-

19v = 266

v = 14.

Now substitute v = 14 in the first equation

3b + 2 (14) = 118

3b = 90

b = 30.