what steps someone would take to use your method (substitution)
and a clear argument stating the reason why your method is better than the other ones. (in other words, come up with a few good sentences that explain why you choose your method and why others should too!)
To use the method of substitution in solving equations, follow these steps:
Step 1: Identify one variable (let's call it "x") in the equation that you can easily isolate so that you have an expression for x in terms of the other variable(s).
Step 2: Substitute the expression from Step 1 into the other equation(s) in the system, replacing the corresponding variable(s) with the expression.
Step 3: Simplify the resulting equation(s) by combining like terms and solving for the remaining variable(s).
Step 4: Substitute the obtained values back into one of the original equations to solve for the remaining variable(s).
Step 5: Check the solution(s) obtained by substituting the values back into both equations. If the values satisfy both equations, then the solution is correct.
Now, let's discuss why the method of substitution can be advantageous compared to other methods like elimination or graphing:
1. Flexibility: The substitution method allows you to choose any variable to isolate and substitute, providing flexibility in deciding which equation or value to work with.
2. Simplification: The substitution method often leads to simplification because you can substitute an expression in terms of one variable into another equation, reducing the number of variables to work with.
3. No need to manipulate equations: Unlike the elimination method, substitution doesn't require you to multiply equations to eliminate a variable. This eliminates the potential for errors that can arise from manipulating and combining equations.
4. Better for nonlinear equations: Substitution is particularly useful for solving systems of equations where one or both equations involve nonlinear functions. In such cases, elimination might not be straightforward, while substitution can still be applied effectively.
Overall, the method of substitution offers flexibility, simplicity, and better applicability for nonlinear systems, making it a reliable choice for solving equations.