System of Equations solve by elimination

Question

If 10 vans and 14 buses carry 634 students, 10 vans and 8 buses carry 418 students, how many students can a van carry? How many students can a bus carry?

Answer 1

x = number of students carried by vans

y = number of students carried by busses

10x + 14y = 634

10x + 8y = 418

subtract second equation from fist

6y = 216

y = 36

36 busses

Answer 2

Hi Ashley

Vans can hold 10 students

Buses can hold 36 students

Let v = vans

Let b = buses

Equation 1

10v + 14b = 634

Equation 2

10v + 8 b = 418

Vans, v can be eliminated by multiplying Equation 2 by -1, then combining it with Equation 1

-10v - 8b = -418

10v + 14b = 634

This yields

6b = 216

Divide both sides by 6 to solve for b

b = 36

Buses can hold 36 students

You can substitute 36 for b in either of the original equations to solve for the number of students vans hold

10v + 14b = 634

10v + 14(36) = 634

10v + 504 = 634

Subtract 504 both sides of the equation

10v = 130

Divide both sides by 10

v = 13

Checking

Equation 1

10v + 14b = 634

10(13) 14(36) = 634

130 + 504 = 634

634 = 634

Equation 2

10v + 8b = 418

10(13) + 8(36) = 418

130 + 288 + 418

418 = 418.

I hope this helps.