Solving Systems – Choose Your Method Objective: Solve systems of equations by choosing the most efficient method.

Methods for Solving Systems of Equations Graphing Method Used when equations are in slope-intercept form (y = mx + b) or standard form (Ax + By = C). This can only be done by hand if the solution consists of whole numbers. Substitution Method Used when one of the equations is already solved for a variable or can be easily solved for one of the variables. Elimination Method Used when the order of like terms in the equations match.

Choose the Method Which method would be the easiest to use to solve the following systems? x – 2y = -6 x – y = 3 2y – x = 6 y = x – 3 y = x – 3 y = 1/2 x + 6 Elimination Substitution Graphing

Solving Systems of Equations Solve the following system of equations: y = -2x + 1 y = -x + 3 What is the best method to use? Graphing The solution to this system is (-2, 5).

Solving Systems of Equations Solve the following system of equations: 3y + x = 6 y – 2x = -5 What is the best method to use? Elimination 2( )  6y + 2x = 12 6y + 2x = 12 y – 2x = -5 3y + x = 6 The solution to this system is (3, 1). 3(1) + x = 6 7y = 7 3 + x = 6 -3 -3 y = 1 x = 3

Solving Systems of Equations Solve the following system of equations: 2x + y = 7 3x = 9 What is the best method to use? Substitution The solution to this system is (3, 1). 3x = 9 2x + y = 7 3 3 2(3) + y = 7 x = 3 6 + y = 7 -6 -6 y = 1

Solving Systems of Equations Solve the following system of equations: 4y = 12 + x x + y = -2 What is the best method to use? Elimination 4y = 12 + x -x + 4y = 12 x + y = -2 4y = 12 + x The solution to this system is (-4, 2). -x -x 4(2) = 12 + x -x + 4y = 12 5y = 10 8 = 12 + x y = 2 -12 -12 -4 = x