Question

Which system is the only inconsistent system?

y = 3x-2
2y = 6x-4
1
O
y = x - 3
y = 3x - 1
y = 3x - 6
y = 3x + 6
y = x - 3
y = -x-1

Answer 1

The only inconsistent system among the given options is y = 3x - 2 and 2y = 6x - 4.

Step-by-step explanation:

The only inconsistent system among the given options is:

y = 3x - 2

2y = 6x - 4

This is an inconsistent system because the two equations do not have a common solution. We can prove this by subtracting the first equation from the second equation:

2y - (3x - 2) = 6x - 4 - (3x - 2)

2y - 3x + 2 = 6x - 3x - 2

2y - 3x + 2 = 3x - 2

2y - 3x - 3x = -2 - 2

2y - 6x = -4

This equation leads to a contradiction since both sides are not equal. Therefore, the only inconsistent system among the given options is y = 3x - 2 and 2y = 6x - 4.

Answer 2

The only inconsistent system is:

2y = 6x - 4

y = 3x - 2

To see this, we can rewrite the first equation as:

y = 3x - 2

Substituting this into the second equation, we get:

y = 3x - 2

This is the same equation as the first equation, so the system has infinitely many solutions.

The other systems given are consistent and either have a unique solution or infinitely many solutions.

Step-by-step explanation: