Consistent Independent - Has 1 solution. Two different equations with different slopes. Lines cross at one point. Only Solution is where the lines cross. Does not pass the vertical line test.
Consistent Dependent - Has infinite solutions. Has many lines with the same slope and same y-intercept and the lines overlap themselves, therefore it is the same line.
Inconsistent - Has no solution. Has two or more lines with the same slope but different y-intercepts. This system of equations does not pass the vertical line test.
While the vertical line test is good, it really doesn't fit this application...the vertical line test is to see if an equation is a function...not this!
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