Solution:
Given, the pair of linear equations are
kx + 3y = k - 3
12x + ky = k
We have to determine the value of k for which the pair of linear equations will have no solution.
We know that,
For a pair of linear equations in two variables be a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0,
If \(\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}\neq \frac{c_{1}}{c_{2}}\), then the graph will be a pair of parallel lines and so the pair of equations will have no solution.
Here, a₁ = k, b₁ = 3, c₁ = k - 3
a₂ = 12, b₂ = k, c₂ = k
So, a₁/a₂ = k/12
b₁/b₂ = 3/k
c₁/c₂ = (k - 3)/k
For no solution,
\(\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}\neq \frac{c_{1}}{c_{2}}\)
So, k/12 = 3/k ≠ (k - 3)/k
Case 1) k/12 = 3/k
k(k) = 3(12)
k2 = 36
k = ±6
Case 2) 3/k ≠ (k - 3)/k
3(k) ≠ k(k - 3)
3k ≠ k2 - 3k
k2 - 3k - 3k ≠ 0
k2 - 6k ≠ 0
k(k - 6) ≠ 0
So, k = 6, 0
Therefore, for the value of k = -6, the pair of linear equations have no solution.
✦ Try This: For which value(s) of λ, do the pair of linear equations λx + y = 2λ/3 and x/2 + λy = 10 have no solution
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 3
NCERT Exemplar Class 10 Maths Exercise 3.3 Problem 2
For which value(s) of k will the pair of equations kx + 3y = k - 3; 12x + ky = k have no solution
Summary:
For the value of k = -6, the pair of linear equations kx + 3y = k - 3; 12x + ky = k has no solution
☛ Related Questions:
- For which values of a and b, will the following pair of linear equations have infinitely many soluti . . . .
- 3x - y - 5 = 0 and 6x - 2y - p = 0, if the lines represented by these equations are parallel. Find t . . . .
- - x + py = 1 and px - y = 1, if the pair of equations has no solution.Find the value(s) of p the pai . . . .
The given pair of linear equations is
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.
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For what value of 'k' the syst...
Updated On: 27-06-2022
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Text Solution
Answer : For no solution, <b> `( k )/(12) = ( 3)/( k ) cancel ( = ) ( 1)/( 2)` <br> `k = +- 6` or `k cancel ( = ) 6` <br> `:. K = - 6`
Answer
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