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, follow these steps:
1. Identify the equation where the substitution method will be applied.
2. Choose one of the variables from the equation and solve it for the given value.
3. Substitute the expression obtained from step 2 into the other equation.
4. Solve the resulting equation to find the value of the remaining variable.
5. Substitute the value obtained in step 4 into either of the original equations to find the value of the last variable.
6. Check the solution by substituting the values back into both original equations.
Now, let's discuss why the method of substitution is an effective choice compared to other methods such as graphing or elimination:
1. Precision: The method of substitution provides the most precise solution as it allows you to directly solve for one variable and substitute it into the other equation. This avoids any potential rounding errors or approximation that may occur while graphing.
2. Versatility: The substitution method can solve systems of equations with more complicated expressions or variables that are difficult to graph accurately. It allows for the substitution of any expression, not just constant values, making it suitable for a wide range of problems.
3. Simplicity: In terms of calculations, substitution often simplifies the equations as you replace one variable with an expression containing fewer terms. This can make the solving process faster and less prone to errors, compared to elimination, which requires additional steps of multiplication and addition/subtraction.
4. Visual Interpretation: While graphing can provide a visual representation of the solution, it may not be as precise or practical when dealing with equations involving fractions, decimals, or irrational numbers. Substitution allows for exact solutions without relying on graphical interpretations.
5. Systematic Approach: The substitution method follows a step-by-step procedure, making it easy to understand and repeat for different equations. It eliminates guesswork and provides clarity in the solving process.
In conclusion, the method of substitution stands out as a versatile, precise, and systematic approach to solving systems of equations. Its ability to handle complex expressions and provide exact solutions makes it a valuable choice for solving a wide range of mathematical problems.