3. 4x + 3y = 12
kx - 2y = 8
a. Write down the condition for No solution
b. Find the value of k
Answers
Answer:
If a pair of linear equations is given by
a1x + b1y + c1 = 0
a2x + b2y + c2 = 0
When the system of linear equations will represent two Parallel Lines there is no point of intersection and consequently there is no pair of values of x and y which satisfy both equation. Thus, system has no solution and such pair of linear equation is inconsistent pair of linear equations
For parallel lines (inconsistent) :
a1 /a2 = b1/b2 ≠ c1/ c2
SOLUTION:
The Given pair of linear equation is :
kx + 3y = k - 3 …………(1)
12x + ky = k……………..(2)
On comparing with General form of a pair of linear equations in two variables x & y is:
a1x + b1y + c1 = 0
and a2x + b2y + c2= 0
a1=k , b1= 3, c= - (k-3)
a2= 12 , b2= k , c= -k
a1/a2= k /12 , b1/b2= 3/k , c1/c2 = -(k-3)/-k
Given: A pair of linear equations will be inconsistent (Parallel) and has no Solution,if
a1 /a2 = b1/b2 ≠ c1/ c2
k/12 = 3/k ≠ -(k-3)/-k……..(3)
(I) (II) (III)
On taking I & II terms
k/12 = 3/k
k × k = 12 × 3
k² = 36
k =√36
k = ±6
Since k = 6 does not satisfy the last two terms of equation 3.
Therefore , k = -6 is the required value.
Hence, for k = - 6 the given system of equations will be inconsistent.
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Step-by-step explanation:
Answer:
a)For no solution, condition is
a1/a2 = b1/b2 not equal to C1/C2
b)As it has no solution above said condition is applied and
4/k=3/-2
Solving this we get
k= -8/3