#320 Find the point of intersection of the two lines

Find the point of intersection of the two - Math

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Free Chegg Question

find the point of intersection of the two lines

L1: x=-2t y=1+2t z+3t

L2: x=-9+5s y=0+5s z=5+1s

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Free Chegg Answer

We then need to find when the components of L1 will be equal to thecomponents of L2:
-2t = -9+5s     (1)
1+2t = 5s      (2)
3t = 5+s         (3)
We then proceed like this: (1) + (2) :
(-2t) + (1+2t) = (-9+5s) + (5s)
1 = -9 + 10s
s = 1
So now we proceed to insert this into L2, where we get that:x = -4, y = 5, z = 6 ,which is the point of intersection of these 2 lines[P(-4,5,6)]: