BASIC COLLEGE ALGEBRA
BASIC COLLEGE ALGEBRA MAC 1105
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This 5 page Class Notes was uploaded by Marquise Graham on Saturday September 19, 2015. The Class Notes belongs to MAC 1105 at University of Florida taught by Staff in Fall. Since its upload, it has received 37 views. For similar materials see /class/207049/mac-1105-university-of-florida in Calculus and Pre Calculus at University of Florida.
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Date Created: 09/19/15
L18 Systems of Equations A system of equations is a set of two or more equations each containing one or more variables The solution set of a system of two equations in two variables is the set of all ordered pairs x y that satisfy both equations Geometrically they are points of intersection of the graphs of the equations Thus the solution set of the system of two equations in two variables is the set of all points of intersection of their graphs if any If a system has at least one solution it is called consistent otherwise it is called inconsistent Systems of Linear Equations in Two Variables A system oftwo linear equations in two variables represents two lines There are three possibilities I The lines intersect at one point 7 one solution the system is consistent and the equations are called independent 2 The lines are coincident 7 in nitely many solutions the system is consistent and the equations are called dependent 3 The lines are parallel 7 no solutions the system is inconsistent We will consider two methods of solving the systems method of substitution method of elimination Example Solve by substitution Graph the equations Example Solve by elimination x 7 5y 7 x 7 2y 5 3xy7 6x2y9 x2y3 2x4y5 Example Solve the system l 2xyl 6x3y3 Computing Wind Speed Traveling against the Wind a cyclist goes 45 miles in 4 hours With the Wind on the return trip he takes 3 hours What is the speed of the cyclist in still air and What is the speed of the Wind Chemist Mixing Solutions A chemist has one solution containing a 10 concentration of acid and the second solution containing a 15 concentration of acid How many ml of each should be mixed in order to obtain 10 ml of a solution containing a 12 concentration of acid Banking A college student has 3000 in two different savings accounts with interest rates of 55 and 6 If his interest per year is 17410 how much is deposited in each account Nonlinear System of Two Equations in Two Variables x2 y2 25 2x 10 A nonlinear system 1s a system of equat1ons 1n y which at least one of the equations is not linear Example Solve the nonlinear systems Graph each equation and show the points of intersection if any y2x yx2l 53944 1 2 3 4 a 198 199