You purchase a drink and a sandwich for $4.50. your friend purchases a drink and five sandwiches for 16.50. you want to determine the price of a drink and the price of a sandwich

The cost of 1 drink   = $0.50

The cost of 1 sandwich  = $4

Step-by-step explanation:

Let the cost of 1 drink = $x

and The cost of 1 sandwich = $y

⇒The The cost of 1 drink + 1 sandwich  =  $x + $ y   = $4.50

or,  $x + $ y = $4.50

or, x + y = 4.50

Also, The The cost of 1 drink + 5 sandwich  =  $x + ($ y)5    =  $16.50

                                                                        or,  x + 5y   =  16.50

⇒   x + 5y = 16.50

Hence, the given system of equations is:

x + y = 4.50

x + 5y = 16.50

Subtract (2) from (1), we get

x + y - (x+ 5y) =  4.50 -  16.50

or, -4y = -12

or, y =  12/4  = 3

Hence, the cost of 1 sandwich  = $4

Now, x + y = 4.50

⇒   x = 4.50 - y = 4.50 - 4  = 0.50

or, x  = 0.50

Hence, the cost of 1 drink   = $0.50