Question

Option 1: There are three ways to solve systems of linear equations: by elimination (sometimes called addition), by substitution, and by creating a graphical representation. In your real-world scenario, discuss advantages and disadvantages of using each of the three ways. Initial posts should include two or more variables (such as the number of boys and the number of girls) and have two or more equations involving those variables (such as there are twice as many girls as boys and that there are 33 children altogether). Response posts in this option should show a solution using one of the three ways.

Answer 1

There are three diferent methods for solving linear equations. We get same answer by solving with any of them but each of them has its own advantages and disadvantages.

Explanation:

The different methods for dolving the linear equations are:

• Substitution
• Elimination
• Graphing

The advantages and disavantages with examples are as follows:

A: Substitution- In this we write an equation for second variable when the first is given which gives an advantage. It is considered best when one or both the equation is solved for any one of the variable.

When we have one of the variable whoes coefficient is 1 it works well.

Example:

Let the equation be

x=
`{10}-{1}`

we can substitute this value in another equation,

Then in that case,

x=
`{-3}*{10}-{y}+{2y}`

=
`{5}-{30}+{3y}+{2y}`

⇒5y=35

⇒y=7.

Now, as we have value for one variable we will substitute it in the first equation given, we will get

x=3.

B: Elimination- It is the best method to use. it is used when both of the given equation are in standard form. It is also used when all the given variables have a coefficient other than 1.

C: Graphical representation- It is best used when a new student is trying to learn equation solving as it gives a visual idea of solving the linear equation. The disadvantages associated with it is that it takes more time than the other two methods and is also less exact. It should be recommended only when we get a question to be solved with a graph.