Are these system of equations consistent, inconsistent, or dependent?

Question

4x + 2y = -6

2x + y = 8

I really do not know how to solve these kinds of problems. I want to know how to solve them without graphing.

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Answer 1 · 2016-09-26T22:51:41

This system of equations is inconsistent.

Notice that if you divide both sides of the first equation by $2$ then you get:

$2x+y = -3$

From the second equation:

$2x+y = 8$

So if both equations hold then $-3 = 8$ , which is false.

So the system of equations is inconsistent.

If you did graph the two equations, then you would get two parallel lines, having no point of intersection.