Question

No Solutions
5-4+7x+1=_x+_
One Solution
5-4+7x+1=_x+_
Infinitely Many Solutions
5-4+7x+1=_x+_

Answer 1

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Answer 2

Given:

5y+7x+1 and _x+_ y + _

To Find:

_x + _y + _ such that there it has :

No solution with 5y + 7x+ 1

One Solution with 5y + 7x + 1

Infinitely Many solution with 5y + 7x +1

Solution:

For both the equations to have no solutions,

• The lines should be parallel.

• _x + _ y + _ = 7x + 5y + k , k ≠ 1 .

For both the equations to have exactly one solution,

• Lines should not be parallel or coincide.
• _x + _y + _ = Ax + By + C , where
• A ≠ 7, B ≠ 5, C ∈ |R.
• A and B should not be a multiple of 7 and 5 simultaneously.
• eg : 14x + 39y + 5 = 0

For both equations to have infinitely many solutions,

• Ax + By + C = (7x + 5y + 1) x n ,
• n ∈ Z , Integers
• eg : 14x + 10y + 2 coincides with 7x + 5y + 1 , has infinitely many solutions.

For both the equations to have no solutions, _x + _ y + _ = 7x + 5y + k , k ≠ 1 .

For both the equations to have exactly one solution, A and B should not be a multiple of 7 and 5 simultaneously.

For both equations to have infinitely many solutions,  Ax + By + C = (7x + 5y + 1) x n ,