Solve the following systems of equations:
Approximate the solutions of the following systems of equations by graphing the functions on a number plane and approximating their points of intersection. Round your values to one decimal place.
The sum of two numbers is 60. The larger number equals the smaller number squared plus 4.
Set up two equations by letting x and y be the two numbers, where y is the larger of the two numbers.
Find all the solutions for x and y. Write your answers as ordered pairs.
In business, supply and demand functions are ways of expressing the supply or demand of a commodity as a function of its unit price. Market equilibrium is the term that describes when the supply is equal to the demand. Consider the supply and demand functions for a new book bag below, where y is in dollars and x is in thousands of units supplied:
Supply function: y = 2 x^{2}
Demand function: y = 4 x + 6
Solve the equations for x.
Which of these values of x must the equilibrium point be at? Explain your answer.
Find the value of y for this value of x.
Complete the following statement:
The equilibrium quantity occurs when ⬚ thousand units are being produced, which has a corresponding price of ⬚ dollars per unit.