The pair of equations 6x – 10y = 7 and - 6x + 10y = 9 have
Answers
Given : The pair of equations 6x – 10y = 7 and – 6x + 10y = 9
To Find : Number of solutions:
(a) a unique solution
(b) infinitely many solutions
(c) no solution
(d) two solutions
Solution:
Pair of linear equations
a₁x + b₁y + c₁ = 0
a₂x + b₂y + c₂ = 0
Consistent
if a₁/a₂ ≠ b₁/b₂ (unique solution and lines intersects each others)
a₁/a₂ = b₁/b₂ = c₁/c₂ (infinite solutions and line coincide each other )
Inconsistent
if a₁/a₂ = b₁/b₂ ≠ c₁/c₂ ( No solution , lines are parallel to each other)
6x – 10y = 7
– 6x + 10y = 9
=> 1/(-1) = -1/1 ≠ 7/9
Hence No solution
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