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# Solve and graph systems of ineqalities in one and two variables.

Instructions #1
Instructions for 1a-b-c-d:

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
[4]
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
[4]
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
[4]
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
[4] 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 Instructions for 1a-b-c-d:

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
[4] 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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