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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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Q: How do you use different techniques to solve linear equations?

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Elimination and substitution are two methods.

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To solve it by coordinate graphs you would take a point from the line and plug in the X and Y value into the equations and or inequalities.

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Elimination and substitution are two methods.

Elimination and substitution are two methods.

There are more than two methods, and of these, matrix inversion is probably the easiest for solving systems of linear equations in several unknowns.

You simplify the brackets first and then you will have linear equations without brackets!

To solve linear equations, you always use the inverse operations

Linear Algebra is a branch of mathematics that enables you to solve many linear equations at the same time. For example, if you had 15 lines (linear equations) and wanted to know if there was a point where they all intersected, you would use Linear Algebra to solve that question. Linear Algebra uses matrices to solve these large systems of equations.

I have never seen the term 'symbolic' used in this way. There are 4 methods used to solve a system of linear equations in two variables. Graphing, Substitution, Elimination, and Cramer's Rule.

Because its linear and the equation is a problem to solve

The answer depends on whether they are linear, non-linear, differential or other types of equations.

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Quality does not normally play any part in linear equations.

If you already know that x = -3 and y = 5 what linear equations are you wanting to solve?

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