Question

You are hoping to start a business and plan to invent a product to sell. If

your presentation is successful, "the Dragons" will invest in your product and
you will be able to start your business. Your first step is to come up with a
product to sell. Consider the following:
The amount it will cost to start-up your business
-The amount it will cost to make each product
-The amount you are going to sell your product for
Using this data, you will create two equations.
Equation 1: Cost: y = mx + b
Where: y = total amount of money it will cost you
m = cost for producing 'x' amount of products
b= fixed start-up cost
Equation 2: revenue: y = (price) x
Where: y = total amount of money you will make
Aa
(price) = the amount you are charging for each product
x = number of products you will sell
Write down your system of linear equations.
Solve your system of equations using the three methods that we have
discussed in class: the Graphing method, the Substitution method, and the
Elimination method.

Worth 150 points in my class, pls help ??

Answer 1

Let's start by writing down the system of linear equations based on the given information:

Equation 1: Cost:
y = mx + b
Where:
y = total amount of money it will cost you
m = cost for producing 'x' amount of products
b = fixed start-up cost

Equation 2: Revenue:
y = (price) x
Where:
y = total amount of money you will make
(price) = the amount you are charging for each product
x = number of products you will sell

To solve the system of equations using different methods, we need more specific values for the variables. Can you provide the values for the cost to produce each product, the fixed start-up cost, and the selling price of each product? Once we have those values, we can proceed with solving the equations using the graphing, substitution, and elimination methods.

Answer 2

Equation 1: Cost: y = mx + b

Where: y = total amount of money it will cost you

m = cost for producing 'x' amount of products

b = fixed start-up cost

Equation 2: Revenue: y = (price) x

Where: y = total amount of money you will make

(price) = the amount you are charging for each product

x = number of products you will sell

To solve this system of linear equations using the three methods discussed in class, we need to first set the two equations equal to each other:

mx + b = (price) x

We can rearrange this equation to solve for x:

mx - (price) x = -b

x(m - (price)) = -b

x = -b/(m - (price))

Now that we have solved for x, we can substitute this value into either of the original equations to solve for y. Let's use Equation 2:

y = (price) x

y = (price) (-b/(m - (price)))

y = -(price) b/(m - (price))

Therefore, the system of linear equations is:

Equation 1: y = mx + b

Equation 2: y = (price) x

Using the Graphing method, we can plot the two equations on a graph and find the point of intersection, which represents the solution to the system. However, since we donot have specific values for m, b, and the price, we cannot graph the equations.

Using the Substitution method, we can solve one of the equations for y and substitute it into the other equation. Let's solve Equation 1 for y:

y = mx + b

Now we can substitute this expression for y in Equation 2:

mx + b = (price) x

Simplifying this equation, we get:

(mx - (price) x) = -b

x(m - (price)) = -b

x = -b/(m - (price))

Now that we have solved for x, we can substitute this value back into either of the original equations to solve for y. Let's use Equation 1:

y = mx + b

y = m(-b/(m - (price))) + b

y = (mb/(price - m))

Therefore, the solution to the system of linear equations is:

x = -b/(m - (price))

y = (mb/(price - m))

Using the Elimination method, we can multiply Equation 1 by (price) and Equation 2 by -m, and then add the two equations together to eliminate y:

(price) y = (price)mx + (price) b

-m y = -(m price) x

(price - m) y = (price)mx - (m price) x + (price) b

(price - m) y = x((priceSorry, it seems that the last part of the equation got cut off in my previous response. Here is the correct version:

Using the Elimination method, we can multiply Equation 1 by (price) and Equation 2 by -m, and then add the two equations together to eliminate y:

(price) y = (price)mx + (price) b

-m y = -(m price) x

(price - m) y = x((price) - m) + (price) b

Now we can solve for y:

y = [x((price) - m) + (price) b] / (price - m)

And we can solve for x by using either Equation 1 or Equation 2:

x = -b/(m - (price))

Therefore, the solution to the system of linear equations is:

x = -b/(m - (price))

y = [x((price) - m) + (price) b] / (price - m)

Again, please note that these equations are general formulas and do not have specific values for m, b, and the price. You will need to substitute specific values into the equations to find the numerical solution.