Click on the selection that answers the following word problem.
Two cups of coffee and one doughnut cost $4.00; two cups of coffee and two doughnuts cost $6.00. If x equals the cost of a coffee and y equals the cost of a doughnut, what are the values of x and y?
2x + y = 4
2x + 2y = 6
To solve for x and y, we can use the given system of linear equations:
2x + y = 4
2x + 2y = 6
We can solve for y by subtracting the first equation from the second equation:
(2x + 2y) - (2x + y) = 6 - 4
2x + 2y - 2x - y = 2
2y - y = 2
y = 2
Now that we know the value of y, we can plug this value back into one of the original equations to solve for x. Let's use the first equation:
2x + y = 4
2x + 2 = 4
2x = 4 - 2
2x = 2
x = 1
Hence, the cost of a cup of coffee (x) is $1.00 and the cost of a doughnut (y) is $2.00.