The graphical representation of a pair of equations 4x + 3y -1 = 5 and 12x + 9y = 15 will be ?
a) parallel lines
b) coincident lines
c) interesting lines
d) perpendicular lines
Answers
Given : pair of equations 4x + 3y -1 = 5 and 12x + 9y = 15
To Find : graphical representation of a pair of equations will be
a) parallel lines
b) coincident lines
c) interesting lines
d) perpendicular lines
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)
4x + 3y -1 = 5
=> 4x + 3y = 6
12x + 9y = 15
4/12 = 3/9 ≠ 6/15
1/3 = 1/3 ≠ 2/5
Hence No solution as lines are parallel to each other
parallel lines
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The graphical representation of a pair of equations 4x + 3y -1 = 5 and 12x + 9y = 15 will be ?
a) parallel lines
b) coincident lines
c) interesting lines
d) perpendicular lines
Additional informatioN
The lines are intersecting and solution is unique
The lines are coincident and there are infinitely many solution.
Then lines are parallel and no solution