Imagine you are in the market for a new home and are interested in a new housing community under construction in a different city. The sales representative informs you that there are 56 houses for sale two floor plans still available. Use x to represent floor plan one and y to represent floor plan two. Write an equation that illustrates the situation.

I think it would be x+y=56

thanks I thought the same. Now the second question is

The sales representative later indicates that there are three times as many homes available with the second floor plan than the first. Write an equation that illustrates this situation. Use the same variables you used in Part A.
I think it would be:
x+3y=56. Is this correct?

I think it would be x+3x=56

because now you have 3x=y

Not quite understanding since the y is only now 3 times more than x so shouldn't the variable stay the same as in the first part when making the equation?

Now using the equations from Part A and Part B. use substitution to determine how many of each type of floor plan is available. Describe the steps you used to solve the problem

I don't think so The second part is giving you a way to solve the problem. so if you find out whay y is then you can find out what x is.

x+y=56

x+3x=56
56/4= 14
x=14
56-14=42
y=42
check 14+42=56 or 14+(14*3)=56

I guess you could write it

x+y=56
4x=56
56/4=x
x=14
14+y=56
56-14=y
y=52
I'm not sure how your teacher would want you to show your work. This way might be the simplest form

thank you. Now using Part A and B what is the intercepts of part A and what are the intercepts of part b? Where would the lines intersect if you solved the system by graphing?