on comparing the ratios of the coefficient find out the pair of
equations x+3y-3=0 and 3x-9y -2=0
is consistent or inconsistent
Answers
Given : pair of equations
x +3y-3=0 and 3x-9y- 2=0
To Find : consistent or inconsistent
Solution:
a₁x+ b₁y=c₁
a₂x+b₂y=c₂
Consistent
if a₁/a₂ ≠ b₁/b₂ ( unique solution)
a₁/a₂ = b₁/b₂ = c₁/c₂ ( infinite solution )
Inconsistent
if a₁/a₂ = b₁/b₂ ≠ c₁/c₂ ( No solution)
x +3y = 3
3x-9y = 2
a₁/a₂ = 1/3
b₁/b₂ = 3/-9 = - 1/3
c₁/c₂ =3/2
1/3 ≠ -1/3
a₁/a₂ ≠ b₁/b₂
Hence consistent and unique solution
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