(ii) Assertion (A): Pair of linear equations 9x+3y+12 = 0, 8x + 5y + 24 =0 have infinitely
many solutions
Reason (R) : Pair of linear equations a ax+by+c = 0, a.x+by+c, = 0 have
infinitely many solutions, if a; b.4
b C2
az
A is true but Ris not true.
b.
R is true but A is not true.
d.
A and R both are true.
C.
A and R both are not true
Answers
Given : Assertion (A): Pair of linear equations 9x+3y+12 = 0, 8x + 5y + 24 =0 have infinitely many solutions
Reason (R) : Pair of linear equations
a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0 have infinitely many solutions,
a1/a2 = b1/b2 = c1/c2
To Find : Comment on Assertion and Reason
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)
Pair of linear equations
a₁x + b₁y + c₁ = 0
a₂x + b₂y + c₂ = 0
a₁/a₂ = b₁/b₂ = c₁/c₂ (infinite solutions and line coincide each other )
Hence Reason is TRUE
9x+3y+12 = 0,
8x + 5y + 24 =0
9/8 ≠ 3/5
Hence unique solution and lines intersects each others
=> Assertion is not True
Option B is correct
R is true but A is not true.
Learn More:
Show that system of equation 3x-5y=11 and 6x-10y=20 is inconsistent
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for what value of a, the pair if linear equation. ax+3y=a-3,12x+ay=a ...
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Answer:
Option B is the correct answer.