Gene G. answered • 05/30/19
Retired Electrical Engineer - ACT Prep, Free Official Practice Tests
The idea behind systems of equations is to eliminate one of two variables so you can solve for the other one.
All you need is two independent equations. (They don't represent the same line when graphed.)
We actually have that.
We have buses (B) and vans (V). There are a total of 231 students.
B = number of buses (25 students each), V = number of vans.(7 students each).
7V+25B = 231
The sneaky one is the relationship between buses and vans. There was one more bus.
B = V+1
We can replace the B in the second equation with (V+1). "Substitute" (V+1) for B.
7V+25B = 231
7V + 25(V+1) = 231
7V + 25V +25 = 231
32V = 231-25 = 206
V = 6.4375
B = 7.4375
V and B must resolve to integers. That is not the case. Check your numbers to see if you got some wrong. If so, fix it. You can see how to solve the problem. Once you have an answer for V. substitute that for the V in either equation and solve for B. Then add V+B to get the answer. If you did copy all of the numbers correctly, the problem is wrong and the non-integer solutions don't make sense.
