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I have a doubt...

I know that the systems of equations:

$$\begin{cases} x+y=4\\ 2x+2y=8 \end{cases}$$

is LD, and:

$$\begin{cases} 3x=4\\ 2y=5 \end{cases}$$

is LI, but what if I have?

$$\begin{cases} x+y=4\\ x+y=0 \end{cases}$$

In this case the equations doesn't make sense, are they classified as LI or LD?

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1 Answer 1

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The equations $x+y=4;x+y=0$ are linearly independent because you cannot use one of them to obtain the other. In other words both yield different graphs. If they were dependent they would produce identical graphs.

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