# Point of intersection of two lines

## Homework Statement

Find the point of intersection of two lines
x = -9 + 5t
y = 1 + t
z = 10 - 4t

and

x = -2 -3t
y = 5 + 2t
z = 5 + 3t

N/A

## The Attempt at a Solution

I have read that you should set two of the equations equal to find the value of t, and that value of t should hold for the third equation, but whenever I do that I get two different values for t, and neither of them hold up in the third equation. What am I doing wrong?

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tiny-tim
Homework Helper
Hi dcramps! Where the two lines intersect, the parameter t will be different on each line. So call the parameter for the second line u, then set two of the equations equal to find the values of t and u. Thanks! Now I have my t and u values, and plugging them into the third equation gives me equality...but where do I go from here? Do I plug them into all of the original equations and use the results as my intersection point?

tiny-tim
Yup! 