# Simulataneous linear equations

• TyErd
In summary, you can eliminate one variable by adding a multiple of the other equation to the second equation.
TyErd
The simultaneous linear equations
mx+12y=24---------------1
3x+my=m------------------2

have a unique solution for m= ?
The answer should be m Є R\{-6,6}

what I tried doing was substituting the 2nd equation into m, expanded, grouped them and factorised but I struck a dead end.

TyErd said:
The simultaneous linear equations
mx+12y=24---------------1
3x+my=m------------------2

have a unique solution for m= ?
The answer should be m Є R\{-6,6}

what I tried doing was substituting the 2nd equation into m, expanded, grouped them and factorised but I struck a dead end.

That's the whole question? Seems like you have 3 unknowns and 2 equations... ?

Yes, that is the whole question.

The problem isn't to solve for m, but to state conditions for which there will be a unique solution for m.

The two equations can be put in an augmented matrix form, like so.
[m 12 | 24]
[3 m | 12]

Do you know how to use matrix operations to row-reduce this augmented matrix?

I've touched on a little bit of matrix operations.
shouldn't it be
[m 12 | 24]
[3 m | m] ?? and from there i wouldn't know where to go.

Right. That 3rd entry in the 2nd row should be m, not 12 as I had.

The basic row operations are
• Exchange two rows
• Replace a row by a multiple of itself
• Add a multiple of one row to another row

I think this is the direction they want you to go in this problem.

okkkk, but i am not very familiar with how to do that.

So going back to the system of equations,

mx + 12y = 24
3x + my = m

is there some multiple of the first equation you could add to the second equation to eliminate a variable? The operations you can apply to your system of equations are exactly the same operations as I listed in my previous post

## 1. What are simultaneous linear equations?

Simultaneous linear equations are a set of equations that contain two or more variables and are solved at the same time.

## 2. How are simultaneous linear equations solved?

Simultaneous linear equations can be solved using various methods such as substitution, elimination, or graphing. These methods involve manipulating the equations to find the values of the variables.

## 3. What is the importance of simultaneous linear equations in science?

Simultaneous linear equations are used in science to model and solve real-world problems such as predicting the growth of populations, analyzing chemical reactions, and understanding the behavior of physical systems.

## 4. Can simultaneous linear equations have more than two variables?

Yes, simultaneous linear equations can have any number of variables. However, the equations must be independent and consistent for a unique solution to exist.

## 5. Are there any limitations to solving simultaneous linear equations?

One limitation is that the equations must be linear, meaning that the variables are raised to the first power and there are no products or powers of variables. Additionally, there must be an equal number of equations and variables for a unique solution to exist.

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