Question

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. 100points

Answer 1

Last one:

4x minus 3y = 16

8x minus 6y = 34

Explanation:

4x - 3y = 16

y =(4x - 16)/3

y = (4/3)x - 16/3

8x - 6y = 34

y =(8x - 34)/6

y = (4/3)x - 17/3

These are two distinct parallel lines, hence will never meet

Therefore no solutions

Answer 2

4 x minus 3 y = 16. 8 x minus 6 y = 34

Explanation:

2 x + 8 y = 15. 4 x + 16 y = 30.

Multiply the first equation by 2

4x +16y = 30

They are identical so they are the same line so there are infinite solutions

2 x - y = 18. 4 x + 2 y = 38.

Multiply the first equation by 2

4x -2y = 36

Add to the first equation

4x -2y = 36

4 x + 2 y = 38.

-----------------------

8x =74

This has a solution

4 x + 7 y = 17. 8 x - 14 y = 36.

Multiply the first equation by 2

8x +14y = 34 add to the second equation

8x +14y = 34

8 x - 14 y = 36.

------------------------

16x = 70

This has a solution

4 x - 3 y = 16. 8 x - 6 y = 34.

Multiply the first equation by -2

-8x + 6y = -32

Add to the second

-8x + 6y = -32

8x - 6y = 34

---------------------------

0 = 2

This is never true so there is no solution