Find values of K for which k has no solution, many solutions a unique solution

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In summary, the problem is asking for values of k that would result in the system of equations having no solution, many solutions, or a unique solution. This can be determined by solving for x and y in terms of k and checking for values that would result in an inconsistent or dependent system. Another way to approach this is through the graphical method, where the equations are plotted as lines and the point of intersection is used to determine the number of solutions.
  • #1
judahs_lion
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Homework Statement



Find values of K for which k has no solution, many solutions a unique solution

Homework Equations



x + ky = 1
kx + y =1


The Attempt at a Solution



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  • #2
What in the world is an expression like

[tex]\frac{\binom{x+ky=1}{kx+y=1}}{y}[/tex]

supposed to mean?

Do you know Cramer's rule? Can you find a k that makes the equations dependent? Inconsistent?
 
  • #3
Method I: Try to solve the system for x and y as a function of k. Now check for which values of k the solution makes no sense (for example, if you have to divide by 0). Those are the values for which the system is inconsistent, so no solutions.

Method II: graphical method. The two equations give two lines in the plane. If the cut at a point, the system is fine. If they're the same line, the system has many solutions. If they're parallel, the system has no solutions.
 
  • #4
The problem statement is shown as
judahs_lion said:
Find values of K for which k has no solution, many solutions a unique solution
It makes more sense as "Find values of k for which the system of equations has no solution, many solutions, a unique solution."
 

1. What does it mean for k to have no solution?

When solving an equation or system of equations, the value of k is the unknown variable. If there is no value of k that satisfies the equation, then there is no solution. This means that the equation cannot be solved and there is no possible value for k that would make the equation true.

2. How can I determine if k has no solution?

To determine if k has no solution, you can substitute different values of k into the equation and see if any of them make the equation true. If none of the values make the equation true, then there is no solution for k. You can also graph the equation and see if there is a point where the graph intersects the x-axis, indicating a solution, or if the graph never intersects the x-axis, indicating no solution.

3. What does it mean for k to have many solutions?

If there are multiple values of k that satisfy the equation, then there are many solutions. This means that there are multiple values of k that make the equation true and can be used interchangeably.

4. How can I determine if k has many solutions?

To determine if k has many solutions, you can again substitute different values of k into the equation and see if there are multiple values that make the equation true. You can also graph the equation and see if there are multiple points of intersection with the x-axis, indicating many solutions.

5. What does it mean for k to have a unique solution?

If there is only one value of k that satisfies the equation, then there is a unique solution. This means that there is only one possible value for k that makes the equation true.

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