Systems of Equations_PLS

Systems of Equations_PLS - Department of Mechanical...

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Department of Mechanical Engineering Systems of Equations ES 140 Section 5 Fall 2006
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Department of Mechanical Engineering Solving sets of linear equations Systems of equations are a set of equations which have several unknowns (the number of equations must always be equal to the number of unknowns). There are three ways to solve these systems: Elimination Substitution Use of Matrices
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Department of Mechanical Engineering Elimination Example: Given 2 linear equations with 2 unknowns x and y: 3x + 4y = 11 (1) 2x + 6y = -10 (2) We will eliminate one of the unknowns by multiplying equation (1) by 2/3 and then subtracting equation (2) from the result.
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Department of Mechanical Engineering Elimination – Suitable for manual calculations only (2/3) X (3x + 4y = 11) 2x + 8y/3 = 22/3 -2x - 6y = 10 0 -10y/3 = 52/3 Multiplying by 3 -10y = 52 y = -5.2 Substituting back into equation (1) 3x + (4 X -5.2) = 11 x = 10.6
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Department of Mechanical Engineering
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Systems of Equations_PLS - Department of Mechanical...

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