You are given the following:

Admission fee for children = $2.00

Admission fee for adults = $6.80

Total admission fees collected = $1,458

Total # of people admitted (children + adults) = 285

Let: x = # of children admitted

y = # of adults admitted

With the given information, we can generate a system of linear equations one of which will yield the total # of people admitted into the park and the other will yield the total admission fees collected.

Since x is the # of children and y is the # of adults, and we know that the total # of people is 285, then we arrive at the following: x + y = 285

Since the admission fee for children is $2.00 per child then the fee for children multiplied by the # of children (x) gives you the fees collected for the children admitted. Similarly, the fee for adults ($6.80 per adult) multiplied by the # of adults (y)
gives you the fees collected for the adults admitted. Adding the fees collected for the children to the fees collected for the adults yields the total admission fees collected ($1,458). That is,

(2.00)x + (6.80)y = 1,458

With this, the system consists of the following equations:

x + y = 285

2x + 6.8y = 1,458

There are a couple of ways to solve for the system, I find the simplest to be the elimination method. Using this method, we eliminate one of the variables by multiplying one of the equations by a constant that will generate a coefficient for the this variable
that is the opposite of the same variable's coefficient in the other equation. For instance, if we choose to eliminate the x variable then we multiply the first equation by -2 to yield -2x which will be eliminated since the second equation has a +2x:

-2(x + y = 285) ==> -2x - 2y = -570

Now we add this equation to the second equation:

-2x - 2y = -570

+ 2x + 6.8y = 1,458

_______________________

0x + 4.8y = 888 ==> 4.8y = 888

Solve for y by dividing both sides of the equation by 4.8:

4.8y/4.8 = 888/4.8

y = 185

Use the answer for y to solve for x by plugging in its value in the first original equation:

x + y = 285

x + 185 = 285

Subtract 185 from both sides of the equation to solve for x:

x + 185 - 185 = 285 - 185

x = 100

Solution: x = 100 and y = 185

Thus, the number of children admitted is 100 and the number of adults admitted is 185.