If x – ky = 2 and 3x + 2y = -5 has unique solution then find k:
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Given :
X - KY = 2
3X + 2Y = -5
Here,
a1=1 ; b1=K ; c1=2
a2=3 ; b2= 2 ; c2= -5
For equation to represent coincident lines
(a1 / a2) = (b1 / b2) = (c1 / c2)
(1 / 3) = (K / 2) = (2 / -5)
We take
1/3 = K/2
K= (1x2) / 3 = K=2/3
X - KY = 2
3X + 2Y = -5
Here,
a1=1 ; b1=K ; c1=2
a2=3 ; b2= 2 ; c2= -5
For equation to represent coincident lines
(a1 / a2) = (b1 / b2) = (c1 / c2)
(1 / 3) = (K / 2) = (2 / -5)
We take
1/3 = K/2
K= (1x2) / 3 = K=2/3
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