Find the value of k for the following system to have no solutions etc?

In summary, the conversation discusses finding the values of k for a system of equations to have no solutions, infinitely many solutions, or a unique solution. The solution is then found and the user is reminded to show their progress in future posts.
  • #1
orgekas
5
0
Find the values of k , if any, for which the following system of equations has
i) no solutions,
ii) infinitely many solutions
and
iii) a unique solution. Solve and find the unique solution.

(k+1)*(X1) + 3*(X2) - (X3) =22

2*(X1) + K*(X2) + (X3) =14

(X1) + 4*(X2) + (X3) =20
 
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  • #2
Hi orgekas! Welcome to MHB! (Smile)

We ask that our users show their progress (work thus far or thoughts on how to begin) when posting questions. This way our helpers can see where you are stuck or may be going astray and will be able to post the best help possible without potentially making a suggestion which you have already tried, which would waste your time and that of the helper.

Can you post what you have done so far?
 
  • #3
Ok. I solved it now I don't any help. Thanks I'll include my working out in my future posts.
Thank you.
 

FAQ: Find the value of k for the following system to have no solutions etc?

What is the purpose of finding the value of k in this system?

The value of k determines the number of solutions or the type of solutions (real or imaginary) in the system. This is important in solving equations and determining the relationship between variables.

Why does the system have no solutions when k is a specific value?

When k is a certain value, it causes the equations in the system to contradict each other, making it impossible to find a solution that satisfies both equations. This results in the system having no solutions.

How can I find the value of k for this system?

To find the value of k, you can use various methods such as substitution, elimination, or graphing. These methods involve manipulating the equations in the system to solve for k.

Can there be more than one value of k that results in no solutions?

Yes, there can be multiple values of k that make the system have no solutions. This is because different values of k can cause the equations to contradict each other in different ways.

What does it mean if the value of k is a complex number in this system?

If the value of k is a complex number, it means that the solutions to the system will involve imaginary numbers. This indicates that the equations in the system do not intersect and the solutions will be complex numbers.

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