Assertion: If the system of equations 2x + 3y = 7 and 2ax + (a + b)y
= 28 has infinitely many solutions, then 2a - b = 0
Reason: The system of equations 3x - 5y = 9 and 6x - 10y = 8 has a
unique solution.
Answers
→ assertion is right and Reason is wrong
Given : Assertion: If the system of equations 2x + 3y = 7 and 2ax + (a + b)y
= 28 has infinitely many solutions, then 2a - b = 0
Reason: The system of equations 3x - 5y = 9 and 6x - 10y = 8 has a
unique solution.
To Find : Correct option
Both A and R are True and R is correct explanation of A
Both A and R are True and R is not correct explanation of A
A is true , R is not true
A is not true , R is true
Both A & R are false
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)
Assertion:
system of equations 2x + 3y = 7 and 2ax + (a + b)y = 28 has infinitely many solutions
=> 2/2a = 3/(a + b) = 7/28
=> 1/a = 3/(a + b) = 1/4
=> a = 4
and a + b = 12
=> 4 + b = 12
=> b = 8
2a - b = 2(4) - 8 = 0
Hence Assertion is TRUE
Reason:
The system of equations 3x - 5y = 9 and 6x - 10y = 8 has a
unique solution.
3/6 = -5/-10 ≠ 9/8
Hence no solution
Reason is not true
Assertion is true , Reason is not true
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