2. As you are leaving the community, you notice another new community just down the street. Because you are in the area, you decide to inquire about it.

a. The sales representative here tells you they also have two floor plans available, but they only have 38 homes still for sale. Write an equation that illustrates the situation. Use x and y to denote floor plan one and floor plan two respectively.

X+y=38

b. The representative tells you that floor plan one sells for $175,000 and floor plan two sells for $200,000. She also mentions that all the available houses combined are worth $7,200,000. Write an equation that illustrates this situation. Use the same variables you used in Part a.

175,000(x)+200,000(y)=7,200,000

c. Use elimination to determine how many houses are available in each floor plan. Explain how you arrived at your answer.

Just need help with part C

First of all, simplify your second equation

175,000(x)+200,000(y)=7,200,000
175x + 200y = 7200
7x + 8y = 288 (#2)
multiply your first equation by 7
7x + 7y = 266 (#1)

(#2) - (#1)
y = 22
then back into original first
x + 22 = 38
x = 16

To determine how many houses are available in each floor plan using elimination, you can manipulate the equations from parts a and b in order to solve for x and y. Here's how you can arrive at the answer:

From part a, the equation is X + y = 38.
From part b, the equation is 175,000(x) + 200,000(y) = 7,200,000.

To use elimination, we need to eliminate one of the variables (either x or y) by multiplying one or both of the equations by suitable numbers so that the coefficients of either x or y in both equations become equal.

In this case, let's eliminate the x variable by multiplying the first equation by 175,000 and the second equation by 1:

175,000(X + y) = 38 * 175,000
175,000X + 175,000y = 6,650,000

175,000(x) + 200,000(y) = 7,200,000

The system of equations now becomes:
175,000X + 175,000y = 6,650,000
175,000(x) + 200,000(y) = 7,200,000

Subtracting the first equation from the second equation:

175,000X + 175,000y - (175,000X + 200,000y) = 6,650,000 - 7,200,000

Simplifying the equation:

-25,000y = -550,000
Dividing both sides of the equation by -25,000 to solve for y:

y = -550,000 / -25,000
y = 22

Now that we have the value of y, we can substitute it back into either of the original equations to solve for x. Let's use the first equation:

X + y = 38
X + 22 = 38
X = 38 - 22
X = 16

Therefore, there are 16 houses available for floor plan one and 22 houses available for floor plan two in the new community.