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When you use the substitution method to solve a system of equations, you do the following.
1. Find an expression for one of the variables in terms of the remaining variables.
2. Use that expression wherever the variable appears in the remaining equations.
3. Using the remaining equations as your new system of equations, repeat from step 1 until there are no more equations.
4. When you have found a value for a variable, work backwards through the chain of substitution expressions until you have values for all of the variables.
An example can be found here.
1. Find an expression for one of the variables in terms of the remaining variables.
2. Use that expression wherever the variable appears in the remaining equations.
3. Using the remaining equations as your new system of equations, repeat from step 1 until there are no more equations.
4. When you have found a value for a variable, work backwards through the chain of substitution expressions until you have values for all of the variables.
An example can be found here.
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