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1. Elimination: Select two equations and a variable to eliminate. Multiply each equation by the coefficient if that variable in the other equation. If the signs of the coefficient for that variable in the resulting equations are the same then subtract one new equation from the other. If they have opposite signs then add them. You will now have an equation without that variable. Repeat will other pairs and you will end up with one fewer equation and one fewer variable. Repeat this process: after each round you will have one fewer equation and one fewer variable. Keep going until you are left with one equation in one variable. Solve that. Then work backwards solving for the other variables.

2. Substitution: Select a equation and a variable. Make that variable the subject of the equation. The right hand side of this equation is an expression for that variable. Substitute this expression for the variable is each of the other equations. Again, one fewer equation in one fewer variable. Continue until you are left with one equation in one variable. Solve that. Then work backwards solving for the other variables.


3. Matrix inversion: If A is the nxn matrix of coefficients, X is the nx1 [column] matrix of variables and B is the nx1 matrix of the equation constants, then X = A^-1*B where A^-1 is the inverse of matrix A.

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โˆ™ 2016-08-08 08:45:30
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Q: How do you use different techniques to solve linear equations?
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