Refer the attachment and please answer with step-by-step explaination only....
Answer both questions please...
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Answers
1)
3x - 9y = 12 { divide by 3 }
x - 3y = 4 ...(1)
On comparing,
a1 = 1 , b1 = -3, c1 = 4
(i) Intersecting:
px + qy = dc ...(2)
on comparing,
a2 = p , b2 = q , c2 = d
For intersecting lines:
a1/a2 ≠ b1/b2
1/p ≠ -3/q
p ≠ 1 , and q ≠ -3
So,
Required linear equation = 2x + y = 1
(ii) coincident
Multiply the equation (1) by 2
Required linear equation:
==> 2x - 6y = 8
(iii) Parallel
ex + fy = gc ...(3)
On comparing,
a3 = e , b3 = f , c3 = g
For Parallel line:
a1/a3 = b1/b3 ≠ c1/c3
a1/a3 = b1/b3 ; b1/b3 ≠ c1/c3
1/e = -3/f ; -3/f ≠ 4/g
e = 1 and f = -3 ; f ≠ -3 and g ≠ 4
Required linear equation:
==> x - 3y = 3
2)
ax + 3y = a - 3 ; 12x + ay = 0
On comparing,
a1 = a , b1 = 3 , c1 = a-3 ; a2 = 12 , b2 = a , c2 = 0
For no solutions, lines must be parallel to each other:
a1/a2 = b1/b2 ≠ c1/c2
a1/a2 = b1/b2 ; b1/b2 ≠ c1/c2
a/12 = 3/a ; b1 c2 ≠ c1 b2
a² = 36 ; 0 ≠ a² - 3a
a = -6, 6 ; a ≠ 3
Hence, value of a are 6 and -6