I recognize this is fairly standard stuff compared to most of the questions right here, but I have to begin somewhere.

You are watching: Three lines that intersect in three points

How would certainly I discover out whether the following lines intersect the very same suggest, and also if so, wbelow is that?

$y - 2x + 3=0$$2x + y - 53=0$$y - x - 11=0$

I"ve review the answers to "How to discover wbelow 3 lines intersect.", yet the answers were as well advanced for me, partly because I"m not discovering thedesigningfairy.com in English.It would certainly be excellent if someone could show me just how they approached this difficulty.


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If you add the first 2 equations, you will uncover that these lines intersect at $y=25$. What is the corresponding $x$ value? Try to do equivalent things for the second and also third equation, and also the initially and third equation. If these lines intersect at the exact same allude, you have to discover the same answers.


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If you at initially look at 2 of the equations and resolve them as a collection of two equations with two unknowns, you will certainly discover out where two of the lines intersect. Then all you need to perform is to examine if the last line also goes via the very same point. (Does the x and also y worths from the first set of equations fit in the last equation?)


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