There are several common methods to solve a system of equations, including substitution, elimination, and graphing. Here is a brief overview of how each method works:
- Substitution Method:
- Solve one of the equations for one variable in terms of the other(s).
- Substitute this expression into the other equation(s).
- Solve the resulting equation for the remaining variable.
- Substitute back to find the value of the other variable(s).
- Elimination Method:
- Write both equations in standard form.
- Multiply one or both equations, if necessary, to get coefficients of one variable as opposites.
- Add or subtract the equations to eliminate one variable.
- Solve for the remaining variable.
- Substitute this value back into one of the original equations to find the other variable.
- Graphing Method:
- Graph both equations on the same coordinate system.
- The solution is the point(s) where the lines intersect.
- This method is more visual and often less precise for exact answers.
For example, to solve by elimination:
- Write equations in standard form.
- Make coefficients of one variable opposites.
- Add the equations to cancel that variable.
- Solve for the remaining variable.
- Substitute the value back to find the other variable.
For substitution:
- Express one variable in terms of the other in one equation.
- Substitute into the second equation.
- Solve for the single variable.
- Use that to find the other variable.
These methods work well for systems of two or three variables depending on the complexity. If more detailed step-by-step instructions or examples are needed for a specific method, they can be provided.
