Point of Intersection between two lines

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Question: Find the point of intersection between two lines:

Line 1: enter image description here and Line 2: enter image description here

I tried doing this question by inputting the x,y,z values from line 2 into line 1 but I got stuck and I don't think I got the correct answer. Can anyone help me out? If so, I'd really appreciate it! Thanks.

This was my most recent attempt to do the question:

enter image description here

As you can see, the answer that I got for s, was 38/13. Which I know is not correct. The area where I highlighted in pink, I feel that's where I messed up but I am not sure. I apologize if the camera quality isn't good.