In the following equations we need to find which one have a unique solution or infinitely many solutions.
(i) x−3y−3=0; 3x−9y−2=0
comparing the given equations, with pair of general equations;
a1x + b1y + c1 = 0
a2x + b2y + c2 = 0
a1/a2 = 1/3, b1/b2 = -3/-9 = 1/3, c1/c2 = 3/2
a1/a2 = b1/b2 ≠ c1/c2
Thus, the pair of equations has no solutions.
(ii) 2x+y=5; 3x+2y=8
comparing the given equations, with pair of general equations;
a1x + b1y + c1 = 0
a2x + b2y + c2 = 0
a1/a2 = 2/3
b1/b2 = 1/2
c1/c2 = 5/8
a1/a2 ≠ b1/b2 ≠ c1/c2
Thus, the given lines have unique solution
