Q1) there are two plans available, but they only have 38 homes available. write an equation that illustrates the situation. use x and y to denote plan 1 and plan 2.

A1) X+Y=38

Q2)Plan 1 sells for $175,000 and plan 2 sells for $200,000. All available houses combined are worth $7,200,000.
What is the equation using same variable from (a).
A2) 175,000X+200,000Y=7,200,000

Q3)Use elimination to determine how many houses in each floor plan available. Explain how you got the answer.
A3) X=38-Y, so you can substitute that into the second equation:
175,000(38-Y)+200,000Y=7,200,000

6,650,000-175,000Y+200,000Y=7,200,000
6,650,000+25,000Y=7,200,000
25,000Y=7,200,000-6,650,000
25,000Y=550,000
Y=22.

So 38-22=16 houses sold for 175,000 and 22 houses for 200,000.

Is this correct?

Yes! Nice work!

good job carmen! way to go!

Yes, your calculations are correct. According to the given equations, there are 16 houses available for Plan 1 (selling for $175,000) and 22 houses available for Plan 2 (selling for $200,000). This means that if you add up the number of houses from both plans (16 + 22), it will equal the total number of available houses, which is 38.