All 294 students in the math club went on a field trip. some students rode in vans which holds 11 students each and some students rode in buses which holds 50 students each. how many of each type of vehicle did they use if there were 9 vehicles total?

For this, I am going to use substitution to find the answer in the system of linear equations.
b=buses
v=vans

11v +50b =294
v+b=9

For the second equation, I am going to multiply it by -11 to eliminate the variable v

11v+50b=294
-11v-11b= -99

Cancel out the variables
39b =195

Divide
195/39b=5b

They took 5 buses

Now that you know b, plug into an equation. I'm going to use the first one
5+v=9
Subtract
9-5=4

They took 4 vans

To check your answers, plug it into the equation you may of not used.
11 (4)+ 50 (5)=294
44+250=294
Tell me if this helps!!!