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Functions and Equations in Two Variables Functions ... - Google Sites
z = f(x, y). Example:ааEvaluate the function for f(4,ан3). f(x, y) = x. 2. + 4y or ... necessary to solve an equatio
Functions and Equations in Two Variables • Notations
• Systems of Linear Equations
• Systems of Nonlinear Equations
• Substitution Methods
Functions of Two Variables or Inputs • Functions with two inputs can be modeled with this notation:
z = f(x, y)
Example: Evaluate the function for f(4, 3).
f(x, y) = x2 + 4y
or
z = x2 + 4y
Functions of Two Variables or Inputs When working with equations with more than one variable, it is sometimes necessary to solve an equation for a variable. A = s2h
Solve for s.
Solutions to linear systems. Is the point (3, 1) a solution to the linear system? 4x y = 13 x y = 4
Find the solution of the system using the graph.
Solutions to nonlinear systems. Are the points (2, 5) and (1, 7) solutions to the nonlinear system? 4x2 y = 11 x y = 3
Solve the linear system a) graphically, b)symbolically, and c) numerically. 2x + y = 0 7x 2y = 3
Special Cases of Linear Systems
• No solution
• Infinite solutions
Solve the nonlinear system a) graphically, b) symbolically, and c) numerically.
x2 + y2 = 9 x + y = 3
Solve the nonlinear system using your calculator. Approximate the solutions to the nearest hundredth. x2 + y = 5 x + y2 = 6
Joint Variation... Let m and n be real numbers. Then z varies jointly as the mth power of x and the nth power of y if a non zero real number k exists such that
z = kxmyn
Example: The variable z varies jointly as the third powers of x and y. If z = 2160 when x = 3 and y = 4, find z when x = 2 and y = 5.
Functions and Equations in Two Variables
Pg 486 585 x 5, 100, 101, 103
Note: Nonlinear Systems can have special cases too!!
