Download 6.3 Solving Linear Systems by Linear Combinations

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...
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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.
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