# Solving and Graphing Systems of Inequalities

Instructions #1

Suppose you are in the market for a new home and are interested in a new housing community under construction in a different city.

1a) The sales representative informs you that there are two floor plans still available, and that there are a total of 56 houses available. Use x to represent floor plan #1 and y to represent floor plan #2.

Write an equation that illustrates the situation.

1b) The sales representative later indicates that there are 3 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.

1c) Use the equations from parts a and b of this exercise as a system of equations.

Use substitution to determine how many of each type of floor plan is available. Show your work.

1d) What are the intercepts of the equation from part a, of this problem?

What are the intercepts from part b of this problem?

Where would the lines intersect if you solved the system by graphing?

Instructions #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.

2a) The sales representative here tells you they also have two floor plans available, but they only have 38 homes available.

Write an equation that illustrates the situation.

Use x and y to denote floor plan #1 and floor plan #2 respectively.

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## SOLUTION This solution is **FREE** courtesy of BrainMass!

Please see the attached file.

Â© BrainMass Inc. brainmass.com December 24, 2021, 7:26 pm ad1c9bdddf>https://brainmass.com/math/algebra/solving-graphing-systems-inequalities-189072