Strategies for Solving Systems of Linear Equations

Reviewing the Strategies for Solving Systems of Linear Equations In this activity, you will review the three strategies for solving systems of linear equations. 1) Graphing 2) Substitution 3) Elimination A "solution" to a system of equations is the (x, y) ordered pair that satisfies both equations. Graphically, it's the point that lies on both lines. Solving Systems of Equations using Graphing 2 -2 4 -4 6 -6 2 -2 4 -4 6 -6 8 -8 10 -10 What is the solution of the linear system of equations? Write your answer using correct ordered pair notation. 2 -2 4 -4 6 -6 8 -8 2 -2 4 -4 6 -6 8 -8 10 -10 What is the solution of the linear system? (4, 0) (0, 4) (-4, 0) (0, -4) Recall: A "solution" is an ordered pair in the form (x,y) that satisfies both equations, or makes both equations true. Is the point (-1, 5) a solution to the given system? Yes y = 4x + 9 y = 2x + 7 No Another technique for solving a system of equationsis by using substitution. In this strategy, an expression for either the "x"or the "y" is substituted in one equation. The result is that you end up rewriting a system of two equations in two unknowns to a single equationin one variable. Solve by Substitution y = -2 4x - 3y = 18 Substitute the appropriate expression into theother equation of this system. 4x-3( ) = 18 The first step is shown. Rewrite the equation and solve for x. Solve the system of equations by substitution. 4x - 3(-2) = 18 4x + 6 = 18 y = -2 4x - 3y = 18 4x = x = Solution: ( , ) Solving Systems of Equations Using ELIMINATION + Solve the system of equations by using elimination. { -2x + 2y = 8 4x - 2y = 6 Solution: x = x = 14 ( , ) 4( ) – 2y = 6 4x - 2y = 6 –2y = – 2y = 6 y = + Solve the system of equations by using elimination. -3x + 18y = 15 3x - 4y = -1 y y = = Solution: 3x – 4( )= -1 ( , ) 3x – 4y = -1 3x – = -1 3x = x = Solve the system of equations by using elimination. + { -2x - 4y = -12 2x + 3y = 9 Solution: ( , ) |

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