Step-by-step explanation:
iv)
Given pair of linear equations in two variables are:
kx-5y = 4 => kx - 5y - 4 = 0
On comparing with a1x+b1y+c1 = 0 then
a1 = k
b1 = -5
c1 = -4
and
3x+6y = 5 => 3x+6y -5 = 0
On comparing with a2x+b2y+c2 = 0 then
a2 = 3
b2 = 6
c2 = -5
Given that
The equations has no solution
=> a1/a2 = b1/b2
=> k /3 = -5/6
On applying cross multiplication then
=> k×6 = 3×-5
=> 6k = -15
=> k = -15/6
=> k = -5/2
v)
2x+3y-6 = 0
On comparing with a1x+b1y+c1 = 0 thena1 = 2
b1 = 3
c1 = -6
(k+1)x+(2k-1)y = 18
=> (k+1)x+(2k-1)y-18 = 0
On comparing with a2x+b2y+c2 = 0 thena2 = k+1
b2 = 2k-1
c2 = -18
Given that The equations has no solution
Given that The equations has no solution => a1/a2 = b1/b2
=> 2/(k+1) = 3/(2k-1)
=> 2(2k-1) = 3(k+1)
=> 4k-2 = 3k+3
=> 4k-3k = 3+2
=> k = 5
iv) k = -5/2
v) k = 5
Let a1x+b1y+c1 = 0 and a2x+b2y+c2 = 0 are pair of linear equations in two variables,
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Step-by-step explanation:
Solution :-
iv)
Given pair of linear equations in two variables are:
kx-5y = 4 => kx - 5y - 4 = 0
On comparing with a1x+b1y+c1 = 0 then
a1 = k
b1 = -5
c1 = -4
and
3x+6y = 5 => 3x+6y -5 = 0
On comparing with a2x+b2y+c2 = 0 then
a2 = 3
b2 = 6
c2 = -5
Given that
The equations has no solution
=> a1/a2 = b1/b2
=> k /3 = -5/6
On applying cross multiplication then
=> k×6 = 3×-5
=> 6k = -15
=> k = -15/6
=> k = -5/2
Therefore, The value of k = -5/2
v)
Given pair of linear equations in two variables are:
2x+3y-6 = 0
On comparing with a1x+b1y+c1 = 0 then
On comparing with a1x+b1y+c1 = 0 thena1 = 2
b1 = 3
c1 = -6
and
(k+1)x+(2k-1)y = 18
=> (k+1)x+(2k-1)y-18 = 0
On comparing with a2x+b2y+c2 = 0 then
On comparing with a2x+b2y+c2 = 0 thena2 = k+1
b2 = 2k-1
c2 = -18
Given that
Given that The equations has no solution
Given that The equations has no solution => a1/a2 = b1/b2
=> 2/(k+1) = 3/(2k-1)
On applying cross multiplication then
=> 2(2k-1) = 3(k+1)
=> 4k-2 = 3k+3
=> 4k-3k = 3+2
=> k = 5
Therefore, The value of k = 5
Answer :-
iv) k = -5/2
v) k = 5
Points to know:-
Let a1x+b1y+c1 = 0 and a2x+b2y+c2 = 0 are pair of linear equations in two variables,