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Introduction to Functions

Mathematics, Grade 6

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• In algebra, two or more equations, called a system of equations, can be solved together. • A system of equations is a set of two or more equations with the same number of variables. • A solution of a system of equations is a set of values that are solutions which satisfy all the equations. y = -3 x – 2 2 x + y = 12 2 x + y = 12 12 – 2 x = -8 + 2 x 12 = -8 + 4 x y = 12 – 2 x y = 12 – 2 (5) y = 12 – 10 y = 2 4 x – 2 y = 16 – 2 x – 2 x y = 2 x – 2 y = -3 x – 2 y = -3 x – 2 y = 2 x – 2 -2 = -2 y = 2 x – 2 Solving Systems of Equations Identifying Solutions The Graphical Method x y -5 -4 -3 -2 -1 1 1 2 3 4 5 2 3 4 5 -1 -2 -3 -4 -5 0 • A system of equations can be solved by graphing all of the equations in the system. Is the ordered pair (0,-2) a solution of the system of equations below? • The solution of a system of equations is the point at which the lines intersect. • The solution set is (5,2) • The ordered pair (0,-2) is a solution of the system of equations. Solve the system of equations: Solve the system of equations: y = 2 x – 2 y = -3 x – 2 -2 = -3 (0) – 2 ? -2 = -2 -2 = 2 (0) – 2 + 2 x + 2 x + 8 + 8 4 x – 2 y = 16 -2 y = 16 – 4 x y = -8 + 2 x – 4 x – 4 x -2 -2 -2 • Solve both equations for y 20 = 4x 5 = x solution (0,-2) ? © Copyright NewPath Learning. All Rights Reserved. 93-4810 www.newpathlearning.com Systems of Equations

\|xiBAHBDy01687ozX • In algebra, two or more equations, called a , can be solved together. • A system of equations is ____________ _____________________________________ _____________________________________ . • A solution of a system of equations is _____________________________________ _____________________________________ . y = -3 x – 2 2 x + y = 12 2 x + y = 12 y = 4 x – 2 y = 16 y = 2 x – 2 y = -3 x – 2 y = -3 x – 2 y = 2 x – 2 y = 2 x – 2 Solving Systems of Equations Identifying Solutions The Graphical Method x y -5 -4 -3 -2 -1 1 1 2 3 4 5 2 3 4 5 -1 -2 -3 -4 -5 0 • A system of equations can be solved by graphing all of the equations in the system. Is the ordered pair (0,-2) a solution of the system of equations below? • The solution of a system of equations is the point at which the lines intersect. • The solution set is Solve the system of equations: Solve the system of equations: 4 x – 2 y = 16 • Solve both equations for y = x Key Vocabulary Terms • algebra • equation • ordered pair • solution set • system of equations • variable © Copyright NewPath Learning. All Rights Reserved. 93-4810 www.newpathlearning.com Systems of Equations

Introduction to Functions

Mathematics, Grade 6

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