Which system of equations is consistent and dependent? a. 3x + 2y = 3 6x + 4y = 6 b. 4x + 6y = 2 4x + 6y = 1 c. 2x + 3y = -6 2x + 3y = -12 d. 5x + 4y = -30 3x - 9y = -18

As per definition, a consistent and independent system has exactly one solution and a consistent and dependent system has an infinite number of solutions.

Now, we know that the equations in a dependent system with infinite number of solutions will have a common factor.

A quick glance reveals that the system with linear equations:

.......(Equation 1)

and ...(Equation 2)

has a common factor of 2. This is because (Equation 2) can be obtained by multiplying (Equation 1) by 2.

Thus, this system of equations represents a consistent and dependent.

Therefore, Option A is the correct answer.

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