I recognize this is relatively basic stuff contrasted to many of the questions here, however I need to start somewhere.

You are watching: Three lines that intersect in three points

How would certainly I find out whether the following lines intersect the very same point, and if so, whereby is that?

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

I"ve read the answers come "How to uncover where 3 present intersect.", but the answers to be too advanced for me, partly because I"m not discovering thedesigningfairy.com in English.It would be great if someone can show me exactly how they approached this problem.

If you include the very first two equations, you will uncover that these lines intersect at \$y=25\$. What is the matching \$x\$ value? try to do comparable things for the 2nd and 3rd equation, and the an initial and 3rd equation. If this lines intersect at the exact same point, girlfriend should discover the same answers.

If friend at first look at two of the equations and also solve them together a collection of 2 equations v two unknowns, girlfriend will find out where two of the lines intersect. Then all you have to do is to inspect if the last line likewise goes with the same point. (Does the x and also y worths from the very first set the equations right in the critical equation?)

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