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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: ( , ) |