Linear algebra stating two lines are coincident How can I say that two lines are coincident to each other? The lines are $x+y=2$ and $2x+2y=4$. My guess would be below. However, is this correct use of math logic? $$x...--prophetes.ai

Linear algebra stating two lines are coincident How can I say that two lines are coincident to each other? The lines are $x+y=2$ and $2x+2y=4$. My guess would be below. However, is this correct use of math logic? $$x+y=2 \iff 2x+2y=4$$ EDIT: Sorry, I made a typo. I indeed did mean $2x+2y=4$ instead of $2x+2x=4$

You have to understand that a point P is in a line, if and only if, the cordinates of P satisfy the line's equation

Take a point $P=(x_0,y_0)$ in $r_1: x+y=2$. So $x_0+y_0=2$

But $$2 \cdot (x_0+y_0)=2 \cdot 2 = 2x_0+2y_0 = 4$$ thus p also belong to $r_2:2x+2y=4$

Therefore, $P\in r_1 \Leftrightarrow P\in r_2$