The last step in solving a system of equations typically involves interpreting or verifying the solution. Here’s a general breakdown of the process leading to the final step:
1. **Choose a Method:** Decide whether to use substitution, elimination, or matrix operations (such as Gaussian elimination) to solve the system.
2. **Solve the Equations:** Perform the necessary algebraic manipulations to find the values of the unknowns.
3. **Plug Back in (if needed):** Substitute the values back into the original equations to confirm they satisfy all equations in the system.
The **last step** can vary depending on the scenario:
- **For a single solution:** Write out the solution clearly, usually in the form of an ordered pair (x, y) or (x, y, z) for systems with two or three variables, respectively.
- **For no solution:** State that the system is inconsistent and has no solutions, often after determining that the equations are contradictory.
- **For infinite solutions:** Describe the solution set, often in terms of a parameter or general expression, indicating that there are infinitely many solutions.
So, the last step is **interpreting or confirming the final solution(s)** based on the method used and the results obtained.
What’s the last step to solving a system of equations
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