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!)
I have no idea why YOU chose substitution. However, here are ideas from a lot of other people.
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the teacher said i had to do substitution she said it was easier
Whether to use substitution or elimination becomes a judgement call. Sometimes one is easier, at other times not.
e.g.
2x + y = 15
3x +7y = 12
In this case , change the first to y = 15-2x and use substution, clearly easier
e.g
3x + 5y = 9
4x - 3y = 20
Here I would NOT use substitution
multiply 1st by 3 and the 2nd by 5 , then add
etc.
If one of variables has a coefficient of 1 or -1, then substitution is a good and quick method, otherwise it is not easier.
To use the method of substitution in solving equations, follow these steps:
1. Step 1: Identify the equation you want to solve and label the variables. For example, let's consider the equation 3x + 2y = 12.
2. Step 2: Solve one of the equations for one variable in terms of the other. In this case, let's solve for x: 3x = 12 - 2y, thus x = (12 - 2y)/3.
3. Step 3: Substitute the expression for the variable you solved in step 2 into the other equation. In our case, substitute x = (12 - 2y)/3 in the equation above.
4. Step 4: Simplify and solve the equation obtained in step 3 for the remaining variable. This will give you the value of y.
5. Step 5: Substitute the found value of y back into one of the original equations to solve for x.
Now, as for why the method of substitution is better than other methods, here are a few arguments:
1. Flexibility: Substitution allows you to solve equations with multiple variables, making it a versatile method. You can solve for any one variable, and then substitute its value into another equation to solve for the rest.
2. Step-by-step process: The method of substitution follows a clear and systematic set of steps, which makes it easier to understand and follow along. It ensures that you can solve equations methodically without missing any crucial steps.
3. Solving complex equations: Substitution is particularly effective in solving complex equations that involve multiple variables, as it allows you to break down the problem into simpler, step-by-step computations.
4. Consistency: The method of substitution is based on the fundamental principles of algebra, ensuring a consistent approach to solving equations. This consistency makes it a reliable and widely accepted method in mathematics.
Overall, the method of substitution is a powerful tool in solving equations. It offers flexibility, a step-by-step process, and the ability to tackle complex problems, making it a preferred choice for many mathematicians and students.