Answer:
Coffee = $2.00
Juice = $1.50
Doughnut = $1.00
Step-by-step explanation:
Given
Let:

So, we have:
Anna

Barry

Cathy

Required
The price of each
We have:



Make c the subject in: 

Substitute
in
and 

![2[5.00 - 3d] + j + 2d = 7.50](https://tex.z-dn.net/?f=2%5B5.00%20-%203d%5D%20%2B%20j%20%2B%202d%20%3D%207.50)

Make j the subject



![3[5.00 - 3d] + j + 4d = 11.50](https://tex.z-dn.net/?f=3%5B5.00%20-%203d%5D%20%2B%20j%20%2B%204d%20%3D%2011.50)

Make j the subject


So, we have:
and 
Equate both values of j

Collect like terms


Substitute
in 




To solve for c, we substitute
in 


Solve for c


In order to utilize the graph, first you have to distinguish which graph accurately pertains to the two functions.
This can be done by rewriting the equations in the form y = mx + b which can be graphed with ease; where m is the slope and b is the y intercept.
-x^2 + y = 1
y = x^2 + 1
So this will be a basic y = x^2 parabola where the center intercepts on the y axis at (0, 1)
-x + y = 2
y = x +2
So this will be a basic y = x linear where the y intercept is on the y axis at (0, 2)
The choice which depicts these two graphs correctly is the first choice. The method to find the solutions to the system of equations by using the graph is by determining the x coordinate of the points where the two graphed equations intersect.