a) The sales representative informs you that there are two floor plans still available, and that there are a total of 63 houses available. The sales representative later indicates that there are six times as many homes available with the second floor plan than the first. Write a system of equations that illustrates this situation. Use x to represent floor plan #1 and y to represent floor plan #2. Translate the problem into two linear equations by identifying keywords that represent a mathematical operation or symbol.
Let's break down the given information step by step:
1. The sales representative informs you that there are two floor plans still available. We can represent the number of houses available for each floor plan as x for the first floor plan and y for the second floor plan.
2. The total number of houses available is 63. This means that the sum of the houses available for both floor plans is 63. So, the first equation we can form is:
x + y = 63
3. The sales representative indicates that there are six times as many homes available with the second floor plan than the first. This means that the number of houses for the second floor plan (y) is six times the number of houses for the first floor plan (x). So, the second equation we can form is:
y = 6x
Therefore, the system of equations that illustrates this situation is:
x + y = 63
y = 6x