Thủ Thuật Hướng dẫn For what value of K the following pair of linear equations has unique solution? Chi Tiết
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The given pair of linear equations is
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- For what value of k the pair of linear equation have unique solution?
- For which value of k will the following pair of linear equations have unique solution 4x KY 8 0 2x 2y 2 0?
- For what value of k will the following system of linear equations have a unique solution KX Y 2 6x 2y 3?
- For what values of k will the following pair of linear equation have unique solution 2x Ky 1 3x 5y 7?
kx + 3y = k – 3 …(i)
12x + ky = k …(ii)
On comparing the equations (i) and (ii) with ax + by = c = 0,
We get,
a1 = k, b1 = 3, c1 = -(k – 3)
a2 = 12, b2 = k, c2 = – k
Then,
a1 /a2 = k/12
b1 /b2 = 3/k
c1 /c2 = (k-3)/k
For no solution of the pair of linear equations,
a1/a2 = b1/b2≠ c1/c2
k/12 = 3/k ≠ (k-3)/k
Taking first two parts, we get
k/12 = 3/k
k2 = 36
k = + 6
Taking last two parts, we get
3/k ≠ (k-3)/k
3k ≠ k(k – 3)
k2 – 6k ≠ 0
so, k ≠ 0,6
Therefore, value of k for which the given pair of linear equations has no solution is k = – 6.
Note: When you get to solve such problems you always need to consider the coefficients of linear equations and perform the operations as done above to get the correct result. Above equations are the equations of two lines and if the lines are parallel then it has no solution because they are not intersecting, if the lines are crossing each other then they have a unique solution and if the lines are coinciding then they have many solutions. Knowing this will solve your problem and will give you the right answers.
For what value of k the pair of linear equation have unique solution?
Hence, for the system of equations to have a unique solution the value of k must not be 6. So, the answer is k can have any value other than 6.
For which value of k will the following pair of linear equations have unique solution 4x KY 8 0 2x 2y 2 0?
Solution. Therefore, for all values of k, except 4, the given pair of equations will have a unique solution.
For what value of k will the following system of linear equations have a unique solution KX Y 2 6x 2y 3?
(d) k≠3 is the correct answer.
For what values of k will the following pair of linear equation have unique solution 2x Ky 1 3x 5y 7?
Thus, k can be any real value except -10/3.
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