Equal Values Method: Isolate the same variable in both equations, set the expressions equal, and solve for the remaining variable. This method reduces a system to a single-variable equation.

Example of Equal Values: For equations $y = x – 1$ and $y = 2x + 3$, set $x – 1 = 2x + 3$, solve for $x$, then substitute back to find $y$.

Substitution Method: Solve one equation for a variable, then substitute this expression into the other equation to simplify.

Example of Substitution: If $y = x – 1$ and $2x + y = 8$, substitute $y = x – 1$ into the second equation to get $2x + (x – 1) = 8$, then solve for $x$ and substitute back to find $y$.

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