# Do these three lines intersect the same point, and if so, where?

I know this is fairly basic stuff compared to most of the questions here, but I have to start somewhere.

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

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

I've read the answers to "How to find where 3 lines intersect.", but the answers were too advanced for me, partly because I'm not learning math in English.
It would be great if someone could show me how they approached this problem.

-
Try thinking of this as a simple three equation system. If you got a solution that satisfies all equations, you got an intersection point. –  kneidell Feb 16 '11 at 11:08

If you add the first two equations, you will find that these lines intersect at $y=25$. What is the corresponding $x$ value? Try to do similar things for the second and third equation, and the first and third equation. If these lines intersect at the same point, you should find the same answers.

-
Even though you didn't exactly show me how, your answer helped a great deal. I used the substitution method to find out the intersection coordinates of each combination of equations to find out that they all intersect the same point (14, 25). Thank you! –  oKtosiTe Feb 16 '11 at 11:36

If you at first look at two of the equations and solve them as a set of two equations with two unknowns, you will find out where two of the lines intersect. Then all you have to do is to check if the last line also goes through the same point. (Does the x and y values from the first set of equations fit in the last equation?)

-