(I know that the questions I answered are right but I'm stuck on c and d. Can someone please help me? I'm not very good at algebra).
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+y(3)=56
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.
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?
c) To solve the system of equations using substitution, we can start with the equation from part a: x + y = 56.
From part b, we can rewrite the equation as x + 3y = 56.
We can solve the first equation (x + y = 56) for x as x = 56 - y.
Now substitute this value of x in the second equation (x + 3y = 56): (56 - y) + 3y = 56.
Simplify the equation: 56 - y + 3y = 56.
Combine like terms: 2y = 0.
Divide both sides by 2 to isolate y: y = 0.
Now substitute this value of y back into the equation x + y = 56: x + 0 = 56.
Therefore, x = 56.
Hence, there are 56 houses with floor plan #1 (x) and 0 houses with floor plan #2 (y).
d) To find the intercepts for the equation from part a (x + y = 56), we can set x = 0 and solve for y.
When x = 0, the equation becomes 0 + y = 56, which simplifies to y = 56.
So the y-intercept is (0, 56).
Now, let's set y = 0 and solve for x.
When y = 0, the equation becomes x + 0 = 56, which simplifies to x = 56.
So the x-intercept is (56, 0).
For the equation from part b (x + 3y = 56), the process is the same.
Setting x = 0 gives 0 + 3y = 56, which simplifies to y = 56 / 3.
So the y-intercept is (0, 56/3).
Setting y = 0 gives x + 3(0) = 56, which simplifies to x = 56.
So the x-intercept is (56, 0).
If you were to graph both equations on a coordinate plane, they would intersect at the point where the lines coincide. In this case, the lines would intersect at the point (56, 0) as that is the common x-coordinate.