7 Assertion (A): Pair of linear equations 9x +3y + 12 = 0 and 18x + 6y +24 =0 have infinitely many solution
Reason(R): pair of linear equations a,x + bịy+ci=0and ax + by + 2, = 0. have infinitely muny solutions if the graphical representation gives coincident line.
class 10
Answers
We have,
9x+3y+12=0...(i)
18x+6y+24=0...(ii)
Here,
a
1
=9,b
1
=3,c
1
=12 and a
2
=18,b
2
=6,c
2
=24
a
2
a
1
=
18
9
=
2
1
;
b
2
b
1
=
6
3
=
2
1
;
c
2
c
1
=
24
12
=
2
1
⇒
a
2
a
1
=
b
2
b
1
=
c
2
c
1
So equations (i) and (ii) represent coincident lines.
Given : Assertion (A): Pair of linear equations 9x+3y+12 = 0, 18x + 6y + 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,
if the graphical representation gives coincident line.
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
graphical representation gives line coincide each other
Hence Reason is TRUE
9x+3y+12 = 0,
18x + 6y + 24 =0
9/18 = 3/6 = 12/24 = 1/2
Hence (infinite solutions and line coincide each other )
=> Assertion is True
Assertion and Reason both are True and Reason is the correct explanation of Assertion.
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