Which of these systems of linear equations has no solution? 2 x + 8 y = 15. 4 x + 16 y = 30. 2 x minus y = 18. 4 x + 2 y = 38. 4 x + 7 y = 17. 8 x minus 14 y = 36. 4 x minus 3 y = 16. 8 x minus 6 y = 34.

The correct answer is:

and

are the equations that have no solution.

Step-by-step explanation:

First of all, let us have a look at the rules for a pair of lines, that have solution or no solution.

Let the equations be:

and

1. There exists exactly one solution:

2. There exists infinitely many solutions i.e. lines are identical.

3. There exists No solutions i.e. lines are parallel and will never intersect.

Now, let us have a look at the given pair of lines:

Option a)

The ratio:

Hence, the lines are identical, infinite solutions.

Option b)

The ratio:

Hence, exactly one solution.

Option c)

The ratio:

Hence, exactly one solution.

Option d)

The ratio:

Hence, There is no solution.

The correct answer is:

and

are the equations that have no solution.