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.

4 x minus 3 y = 16. 8 x minus 6 y = 34 has no solution

Step-by-step explanation:

Examine the system

2 x + 8 y = 15

4 x + 16 y = 30

We see that these equations are identical except for a factor of 2, and thus recognize that this system has infinitely many solutions.

Next, look at the system

2 x minus y = 18

4 x + 2 y = 38

If we divide the second equation by 2, we get the system

2x - y = 18

2x + y = 19

Combining these two equations, we get 4x = 37, which has a solution.

Third, analyze the system

4 x + 7 y = 17                =>  8x + 14y = 34

8 x minus 14 y = 36      => 8x - 14y  = 36, or 16x = 70, which has a solution

Finally, analyze the system

4 x minus 3 y = 16    => -8x + 6y = -32

8 x minus 6 y = 34   =>  8x  - 6y  = 34

If we combine these two equations, we get 0 + 0 = 2, which is, of course, impossible.  This system has no solution.