At the coffee shop, two coffees and one latte cost $10.50. three coffees and two lattes cost $17.00. what is the cost of one coffee?

Let the price of coffee be x and the price of latte be y.
Thus forming the equations given the information we shall have:
2x+y=10.50
y=10.50-2xi
3x+2y=17ii
plugging i in ii we get:
3x+2(10.50-2x)=17
3x+21-4x=17
3x-4x=17-21
-x=-4
thus
x=4
Thus the cost of coffee is $4
thus the cost of latte will be:
y=10.50-2(4)
y=10.50-8
y=2.5
Price of latte is $2.5