Question

the pair of equations x+2y+5=0 and -3x_6y+1=have

Answer 1

Answer:

the pair of equations are parallel and they have no solutions

Answer 2

The pair of equations x+2y+5=0 and -3x-6y+1= 0 have no solutions.

Given:

The pair of equations x+2y+5=0 and -3x-6y+1= 0

To Find:

Number of solution of  pair of equations.

Solution:

Condition for no. of solutions:

unique solution: a₁/a₂ ≠ b₁/b₂

No solution : a₁/a₂ = b₁/b₂ ≠ c₁/c₂

Infinite solutions : a₁/a₂= b₁/b₂ = c₁/c₂

Now consider pair of equations  x+2y+5=0 and -3x-6y+1 = 0

a₁/a₂= 1/-3

b₁/b₂ = 2/-6

c₁/c₂ = 5/1

therefore,

a₁/a₂ = b₁/b₂ ≠ c₁/c₂

so equations have no solution.

Hence, the pair of equations x+2y+5=0 and -3x-6y+1= 0 have no solutions.