Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

How to find the point of intersection of two lines ?

Let's say $2x+y=5$ and $3x+2y=5$ ?

Thanks

share|improve this question
    
Have you encountered systems of equations until now? Finding the intersection of two lines means solving the system of equations determined by those two lines. –  Beni Bogosel Jun 29 '11 at 7:44

1 Answer 1

up vote 3 down vote accepted

The graphs of two lines intersect at a point $(s,t)$ when the point $(s,t)$ is on both lines.

The point $(s,t)$ lies on the line $ax+by=c$ when $as+bt=c$.

Thus, to find the intersection of two lines $ax+by=c$ and $dx+ey=f$ (if it exists), we want to look for a pair of numbers $s$ and $t$ for which $$as+bt=c\qquad\text{and}\qquad ds+et=f.$$

In your example, we want to find an $s$ and $t$ for which $2s+t=5$ and $3s+2t=5$.

Note that if $2s+t=5$, then $t=5-2s$. Substitute this in for $t$ in the expression $3s+2t=5$ to find the value for $s$. Then solve for $t$ using the fact that $t=5-2s$.

share|improve this answer
    
ahah i didnt knew that the point of intersection is the same as the point we get when we solve it. Anyways thanks :) :) –  kritya Jun 29 '11 at 7:43
2  
@kritya: No problem. The correspondence between the graph of a line (or any function), and its equation, is a very important one. –  Zev Chonoles Jun 29 '11 at 7:46

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.