Classify the system 2x + 3y = 6 and 4x + 6y = 12 by choosing the correct label.

Consistent and independent — the two lines intersect at exactly one point because doubling an equation always produces a distinct line that crosses the original.

Consistent and dependent — the two equations represent the same line, so there are infinitely many solutions.

Indeterminate — the system does not meet the definition of linearity because the coefficients form a singular matrix, which precludes classification as consistent or inconsistent without additional information.

Inconsistent — the lines are parallel with the same slope but different intercepts, so there are no solutions.