15 points
for a community breakfast there should be at least
three times as much regular coffee as decaffeinated
coffee. a total of ten gallons is sufficient for the
breakfast. write and graph a system of inequalities
to model the problem.
show your work.

The system of inequalities is x ≥ 3y and x + y ≤ 10

The graph attached down

Step-by-step explanation:

* Lets explain how to write the inequalities for this problem

- Assume that x represents the quantity of regular coffee and

 y represents the quantity of the decaffeinated  coffee

- For a community breakfast there should be at least  three times as

 much regular coffee as decaffeinated  coffee

- At least means greater than or equal

∵ x represents regular coffee

∵ y represents decaffeinated  coffee

∵ x is at least three times as much as y

∴ x ≥ y ⇒ (1)

- A total of ten gallons is sufficient for the  breakfast

- That means the quantities x and y shouldn't be more than 10

- Not more than means smaller than or equal

∵ The total quantity is 10 gallons

∴ x + y ≤ 10 ⇒ (2)

∴ The system of inequalities are

   x ≥ 3y and x + y ≤ 10

* Lets graph (1) and (2)

- The red part for x ≥ 3y

- The blue part for x + y ≤ 10

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3

the first option is the answer.