School A rented and filled 5 vans and 9 buses with 499 students. School B rented and filled 10 vans and 9 buses with 539 students. How many students can a van carry? How many students can a bus carry?

The Number of students:

A van can carry = x = 8 students

A bus can carry = y = 51 students

Step-by-step explanation:

Let us represent

Number of students:

A van can carry = x

A bus can carry = y

School A rented and filled 5 vans and 9 buses with 499 students.

5x + 9y = 499 Equation 1

School B rented and filled 10 vans and 9 buses with 539 students.

10x + 9y = 539 Equation 2

Combining both Equations

5x + 9y = 499 Equation 1

10x + 9y = 539 Equation 2

Using Elimination method

Subtract Equation 2 from 1

-5x = - 40

x = -40/-5

x = 8 students

Solving for y using Equation 1

5x + 9y = 499 Equation 1

5 × 8 + 9y = 499

40 + 9y = 499

9y = 499 - 40

9y = 459

y = 459/9

y = 51 students

Therefore,

The Number of students:

A van can carry = x = 8 students

A bus can carry = y = 51 students

guess at question:

a vertical line intersects the graph of g(x,y) = 0 at two points. what conclusion follows about the function f(x) implicitly defined by g(x,f(x)) = 0?

the domain of f(x) cannot include the x coordinate of any such vertical line.

informally, f(x) is not a function, and

g(x,y)=0 cannot be solved for y uniquely.

the relation r = {(x,y) such that g(x,y) = 0} is a function if

for all (a,b) ∊ r and (c,d) ∊ r, a=c implies b=d.

step-by-step explanation: