Question 143562: Just need help with d), unless of course the others are wrong. Which very well could be. Any help would be of help. Thank you.
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?
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.
a) 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. x + y = 56
b) 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. x = 1x y = 3x
c) Use the equations from part 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. Describe the steps you used to solve the problem. x = 14 y = 42
d) 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?
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website! You sort of have the right idea, but your equation in part b should have been  . You got the correct solution to part c, but you didn't explain the steps to solving by substitution -- namely take the expression in x that is equal to y from the part b equation and substitute into the first equation, then solve for x. After solving for x, use either equation to solve for y.
To determine the intercepts, and I'm supposing that you are talking about the y-intercepts, solve each equation for y.  so  . Now the equation is in slope-intercept ( ) form where m is the slope (-1 in this case), and b is the y-coordinate of the y-intercept (56 in this case - meaning that the line intersects the y-axis at (0,56)). Your second equation is already in slope-intercept form, is the same as  , so the slope is 3 and the intercept is 0 (the intercept is at the origin). The point of intersection you will get by graphing the system is defined by the ordered pair created from the x and y values you calculated in part c of the problem, namely (14,42)
If my supposition was incorrect and you actually need both the x- and y-intercepts, then solve each equation for x. The constant term that results will be the x-intercept.
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