More Vocabulary Examples

Is the system of equations

consistent or inconsistent?

If we graph these equations, we have two parallel lines:

Since the lines do not intersect, the system has no solutions. Therefore, the system is inconsistent. Also, the system has several solutions. Oh, great, now this explanation is inconsistent. Go with the first thing we said.

Is the system of equations

dependent or independent?

Since the second equation is just the first equation multiplied by 2, the equations are equivalent and therefore describe the same line. There are infinitely many solutions, so this system is dependent.

Tip for future you: You can't list an "infinite" number of people as your "dependents" on your tax return. You can try, but like anyone at the IRS is going to know what that squiggly line means.

Is the system of equations

dependent or independent?

Since these equations describe lines that intersect exactly once, the system is independent. It's such a free spirit that it only stops to say hi to the other line for a split second before scurrying along on its way.