Solving Systems by Substitution

A system of equations is a set of two (or more) equations with the same variables. The solution is the values of the variables that make both equations true at the same time. Graphically, the solution is the point where the two lines intersect. [formula] The solution is the point (x, y) that satisfies both equations simultaneously.

When to use: when one equation already has a variable isolated (e.g., y = ...) or can easily be solved for one variable. Steps: 1. Isolate one variable in one equation (if not already done) 2. Substitute that expression into the other equation 3. Solve the resulting one-variable equation 4. Back-substitute to find the other variable 5. Check your answer in both equations

Example: Solve the system: [formula]