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Solving linear equations by substitution is a method used to find the values of variables in an equation system. This method involves solving one of the equations for one variable and then substituting that expression into the other equations.

Basic Steps

The basic steps for solving linear equations by substitution are as follows:

1. Choose one of the equations and solve it for one variable in terms of the other variables.

2. Substitute the expression found in step 1 into the other equations.

3. Solve the resulting equations for the remaining variables.

4. Check the solutions obtained by substituting them back into the original equations to verify their correctness.

Example

Let's solve the following system of linear equations by substitution:

From the first equation, we can solve for $$y$$:

Now, we substitute this expression for $$y$$ into the second equation:

Solving this equation gives us the value of $$x$$. Once we have the value of $$x$$, we can substitute it back into the expression we found for $$y$$ to find the value of $$y$$.

Solving linear equations by substitution is a useful technique for finding solutions to systems of equations when the equations are linear.