3. The co-efficient of pair of linear equations are in proportional then it has unique solution. True /false Explain how?
Answers
Given : . The co-efficient of pair of linear equations are in proportional then it has unique solution.
To Find : True /false
Solution:
The co-efficient of pair of linear equations are in proportional then it has unique solution. - FALSE
The co-efficient of pair of linear equations are in proportional then it has Infinite many solutions as they both represent same line.
ax + by + c = 0
kax + kby + kc = 0 => k(ax + by + c) = 0 => ax + by + c = 0
Hence both represent same line as k ≠ 0
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 )
a₁/a₂ = b₁/b₂ = c₁/c₂ => co-efficient of pair of linear equations are Proportional
Inconsistent
if a₁/a₂ = b₁/b₂ ≠ c₁/c₂ ( No solution , lines are parallel to each other)
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