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Question
solve each equations through elimination.

-6x+6y=6
-6x+3y=-12

Answer
You have 2 unknowns (x and y) and 2 independent equations (trust me on the independence) so you know you can get a solution. The approach is to use one eqn to solve for x in terms of y (or y in terms of x) and then substitute this expression for x (or y) into the 2nd eqn to solve for y (or x). Then finally calculate x (or y).

First, divide all the terms in the 1st eqn by 6 to get -x+y=1 or x = y-1; substitute this into the 2nd eqn (after dividing by 3) to get

-2(y-1)+y=-4 or -y+2=-4 or y=6

substituting this into x=y-1 gives x=6-1=5

so y=6 and x=5.  

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randy patton

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college mathematics, applied math, advanced calculus, complex analysis, linear and abstract algebra, probability theory, signal processing, undergraduate physics, physical oceanography

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26 years as a professional scientist conducting academic quality research on mostly classified projects involving math/physics modeling and simulation, data analysis and signal processing, instrument development; often ocean related

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J. Physical Oceanography, 1984 "A Numerical Model for Low-Frequency Equatorial Dynamics", with M. Cane

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M.S. MIT Physical Oceanography, B.S. UC Berkeley Applied Math

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