Choose from the following list the word that best completes...

Choose from the following list the word that best completes each statement. Not all words will be used. $$\begin{array}{ll}{\text { consistent }} & {\text { opposite }} \\ {\text { elimination }} & {\text { substitution }} \\ {\text { inconsistent }}\end{array}$$ To use the ______ method, a variable must be isolated.

Choose from the following list the word that best completes each statement. Not all words will be used.
$$\begin{array}{ll}{\text { consistent }} & {\text { opposite }} \\ {\text { elimination }} & {\text { substitution }} \\ {\text { inconsistent }}\end{array}$$
To use the ______ method, a variable must be isolated.

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Key Concepts

Variable Isolation

Variable isolation involves rearranging an equation so that one particular variable is on one side of the equation by itself. This process is a crucial step in the substitution method, as it creates a clear expression that can be substituted into other equations. Isolating a variable simplifies the system, making the subsequent steps in solving the equations more straightforward.

Substitution Method

The substitution method is a technique for solving a system of equations where one equation is manipulated to express one variable in terms of the others. This isolated variable expression is then substituted into the other equations. This method is particularly effective when one of the equations can be easily solved for one variable, facilitating a step-by-step reduction of the system.

Systems of Linear Equations

A system of linear equations is a collection of two or more linear equations involving the same set of variables. Solving these systems involves finding values for the variables that satisfy all equations simultaneously. They form the basis for many algebraic techniques used in mathematics and applied sciences, where consistency and the methods of finding a solution are key considerations.

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