Complete both parts. a) What are the three methods used for solving systems of e

Question

Complete both parts.

a) What are the three methods used for solving systems of equations? Which method do you prefer to use?

b) Break-Even Analysis – Systems of Equations Application Problem

Suppose a company produces and sells pizzas as its product. Its revenue is the money generates by selling x number of pizzas. Its cost is the cost of producing x number of pizzas.

Revenue Function: R(x) = selling price per pizza(x)
Cost Function: C(x) = fixed cost + cost per unit produced(x)

The point of intersection on a graph of each function is called the break-even point. We can also find the break-even point using the Substitution Method.

Suppose Dan’s Pizza Parlor has a fixed cost of $280 and it costs $4 to produce each pizza. Dan sells every pizza for $12.

The Revenue Function is: R(x) = 12x
The Cost Function is: C(x) = 280 + 4x

The break-even point occurs where the graphs of C and R intersect. Therefore, we can find this point by solving the system:
y =12x
y = 280 + 4x

How many pizzas does Dan have to produce to break-even? If he exceeds his break-even point, will he make a profit or have a loss?

Explanation / Answer

The three methods most commonly used to solve systems of equation are substitution, elimination and graphing

here we prefer substitution method

y =12x
y = 280 + 4x

now substitute value of y=12x in y=280+4x

12x=280+4x

8x=280

x=35

he have to make 35 pizzas does Dan have to produce to break-even

if he excess breakeven it will make profit

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