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November 18, 2014 6.3 6.3 Solving Linear Systems by Linear Combinations Objective: Solve linear systems using linear combinations. Add the following: + 5x + 2y = 3 -5x + 3y = 7 Linear Combination - 2 equations combined by adding one equation (or multiple of) to the other equation. November 18, 2014 Steps for solving using Linear Combination: 1) Arrange the equations with like terms in columns. 2) Multiply one or both equations by a # to get opposite coefficients for 1 variable. 3) Add equations from Step 2, so one variable cancels out, and solve. 4) Substitute value back into either of original equations. 5) Check the solution. Ex: Solve the following... 1 3 2 x - 2y = 8 x + 6y = -16 5x - 4y = 3 2x + 8y = -2 3x = -6y + 12 -x + 3y = 6 Try: A landscape designer uses 2 types of gravel for walkways. The larger gravel weighs an average of 40 lbs/ft and the smaller weighs an average 48 lbs/ft . In his truck, he has a 12ft -load of gravel that weighs 520 lbs. Is there a mixture of small and large gravel in the truck? If so how many ft of each type. 3 3 3 3