#### Answer

2 large coffees and 3 regular coffees.

#### Work Step by Step

Form two equations using the information given.
Let
$x=$ number of regular coffees
$y=$ number of large coffees.
There are a total of five coffees purchased so:
$x + y = 5$ (Equation 1)
A regular coffee cost 1 dollar while a large costs 1.5 dollars.
The total cost is 6 dollars therefore the equation that represents these is:
$ (1)x + 1.5y = 6$
$\\x + 1.5y=6$ (Equation 2)
The system is:
$x+y=5$ (Equation 1)
$\\x+1.5y=6$ (Equation 2)
Subtract Equation 1 to Equation 2 so $x$'s are eliminated:
$x + 1.5y - (x + y) = 6 - (5)
\\0.5y = 1$
Multiply both sides by 2.
$0.5y(2) = 1(2)$
$y = 2$
Substitute $y = 2$ back into $x + y = 5$
$x + (2) = 5$
Solve by subtracting 2 from each side
$x + 2 - 2 = 5 - 2$
$x = 3$
Therefore they bought 2 large coffees and 3 regular coffees.