At the Holiday Valley Ski Resort, skis cost $16 to rent and snowboards cost $19. If 28 peopie rented on a certain day and the resort brought in $478, how many skis and snowboards were rented?

Assume, there were #X# skis and #Y# snowboards rented.
Since there were #28# people who rented equipment, we have the first equation:
#X+Y=28#

Considering the price of #$16# per ski and #$19# per snowboard, and the total amount resort has got is #$478#, we have the second equation:
#16X+19Y=478#

To solve this system of two linear equations with two unknowns, we will use the method of substitution - resolve the first equation for #Y# in therms of #X# and substitute it into the second equation, thus getting one equation with one unknown.

From the first equation, adding #-X# to both sides, we get:
#-X+X+Y=-X+28#
or, cancelling #-X+X# because it's equal to 0,
#Y=-X+28=28-X#

Substitute this expression for #Y# into the second equation:
#16X+19(28-X)=478#
Using distributive law #a(b+c)=ab+ac#, the latter is:
#16X+19*28-19X=478#
Using commutative law of addition, we can change the sequence of operation. Also, perform the multiplication:
#16X-19X+532=478#

Using the distributive law, we can combine #16X-19X#:
#(16-19)X+532=478#

Subtract #478# from both sides of this equation and perform #16-19# operation:
#-3X+532-478=478-478#
or
#-3X+54=0#
Adding #3X# to both sides yields:
#3X-3X+54=3X#
or
#54=3X#

Dividing by #3# both sides of this equation,
#18=X#

From this we can find #Y=-X+28#:
#Y=-18+28=10#

CHECKING:
#18# (skis) #+# #10# (snowboards) = #28# (CHECK!)
#18*$16= $288# (skis total)
#10*$19=$190# (snowboards total)
#$288+$190=$478# (total rent) (CHECK!)