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pre-calc sect. 7.2-3.3

# pre-calc sect. 7.2-3.3 - Section 7.2 Systems of Linear...

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Section 7.2 Systems of Linear Equations in Three Variables Three equations all of which can be written in the form Ax + By + Cz = D are called a system of linear equations in three variables or a linear system in three variables . A solution to a system of linear equations in three variables is an ordered triple that satisfies all equations in the system. solution: (x,y,z) Ex. (5, -3, -2) is a solution to the system - = + + = - + = + + 1 2 4 3 5 3 2 0 z y x z y x z y x Since 5+(-3)+(-2)=0 is true and 5+2(-3)-3(-2)=5 is true and 3(5)+4(-3)+2(-2)=-1 is true. EX 1: Determine if the given ordered triple is a solution of the system. (-1, -4, 5) - = - + = - - = + - 32 5 3 5 3 2 22 3 2 z y x z y x z y x Solving Linear Systems in Three Variables by Eliminating Variables 1.) Reduce system to two equations in two variables by taking two different pairs of equations and eliminating the same variable from both pairs. 2.) Solve the resulting system of two equations in two variables using addition/substitution. This results in equation in one variable that gives the values of that variable. 3.) Substitute the value of the variable from 2.) into either equation in two variables to find the value of the second variable. 4.) Use the values of the two variables from 2.) and 3.) to find the value of the third variable by substituting into one of the original equations. 5.) Check the solution in each original equation. EX 2: Solve = + - = - - - = - + 6 3 2 5 3 3 1 2 2 z y x z y x z y x

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EX 3: - = + - = + + = - 1 2 3 2 17 2 7 2 z y x z y x z y EX 4: - = + = - + - = - ) 2 ( 3 5 4 4 7 3 5 ) 3 ( 2 3 7 y x z x z y y x z EX 5: Find the quadratic function c bx ax y + + = 2 whose graph passes through (1,4), (2, 1), and (3, 4)
Section 3.1 Exponential Functions Def : the exponential function f with base b is defined by or x b y = , where b is a positive constant other than 1 and x is any real number. Ex. Evaluating and Exponential Function EX 1: The exponential function 1 ) 967 . 0 ( 49 . 13 ) ( - = x x f describes the number of O – rings expected to fail, f(x) , when the temperature is x degrees F.

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pre-calc sect. 7.2-3.3 - Section 7.2 Systems of Linear...

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