Which system has no solutions?

x-y = 0

y = x

2 x + 4y = 9

4x + 2y = 9

3x+y=5

- 3 x - y = 2

5x - y = - 1

- 5y = - 4

A system with no solutions means that there is no possible values of x and y that will fulfill the equations

x-y=0 can be rearranged as x=y+0 which is the same as x=y which is the same as y=x. This system has an infinite amount of solutions, given that x and y have the same value

2x + 4y = 9 can be rearranged as 2x = 9 - 4y which is the same as x = 4.5 - 2y. We can use this value of x in the second equation:

4x + 2y = 9

4 (4.5 - 2y) + 2y = 9

18 - 8y + 2y = 9

18-6y=9

-6y=-9

y=1.5

We now substitute y into the equation to find x

4x + 2y = 9

4x + 2 (1.5) = 9

4x + 3 = 9

4x = 6

x=1.5

This system does have a solution of 1.5, 1.5

-5y = - 4

y = 4/5

5x - y = - 1

5x - (4/5) = - 1

5x = - 1 + 4/5

5x = 1/5

x = 1/25

This system has a solution of 1/25, 4/5

3x+y=5

y = 5 - 3x

-3x - y = 2

-3x - (5 - 3x) = 2

-3x - 5 + 3x = 2

-3x + 3x = 7

0=7

This system does not have a solution