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Systems of Equations

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