given the linear equation 4x+6y-9=0, another linear equation in two variable such that the geometrical representation of the pair , so formed will be consistent is :
[i] 2x+3y-9=0 [ii] 5x-6y-9=0 [iii] 8x+12y-18=0 [iv] 12x+18y-18=0
[a] only [ii] and [iii] [b] none of the above [c] all of the above [d] only [i] and [iv]
Answers
Answer:
a) Only ii and iii
Step-by-step explanation:
Consistent means having intersecting or coincident pair of linear equations.
So,
(ii) 4/5 ≠ 6/-6 or -1 (Intersecting)
(iii) 4/8 or 2 = 6/12 or 2 = -9/-18 or 2 (Parallel)
Hope it helps
Given : linear equation 4x+6y-9=0,
another linear equation in two variable such that the geometrical representation of the pair , so formed will be consistent is :
[i] 2x+3y-9=0 [ii] 5x-6y-9=0 [iii] 8x+12y-18=0 [iv] 12x+18y-18=0
To Find : Choose correct option:
[a] only [ii] and [iii] [b] none of the above [c] all of the above [d] only [i] and [iv]
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+6y-9=0,
[i] 2x+3y-9=0
4/2 = 6/3 ≠ -9/-9
2 = 2 ≠ 1 inconsistent
4x+6y-9=0,
[ii] 5x-6y-9=0
4/5 ≠ 6/-6
Consistent ( unique solution )
4x+6y-9=0,
[iii] 8x+12y-18=0
4/8 = 6/12 = -9/-18
1/2 = 1/2 = 1/2
consistent ( infinite solution)
4x+6y-9=0,
[iv] 12x+18y-18=0
4/12 = 6/18 ≠ -9/-18
1/3 = 1/3 ≠ 1/2 inconsistent
a] only [ii] and [iii] is the correct answer
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