The graph of the pair of linear equations represented by the equations 3x – 5y = 11 and 6x –10y = 7 are __________ .
Answers
Answer:
the type of graph of the pair of linear equations :
3x-5y=11 , 6x-10y=7. is parallel lines.
Given : 3x - 5y = 11, 6x – 10y = 7
To Find : type of the graph of the pair of linear equations
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)
3x - 5y = 11,
6x – 10y = 7
a₁/a₂ = 3/6 = 1/2
b₁/b₂ = -5/-10 = 1/2
c₁/c₂ = 11/7
1/2 = 1/2 ≠ 11/7
a₁/a₂ = b₁/b₂ ≠ c₁/c₂ ( Inconsistent , No solution , lines are parallel to each other)
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