SOLUTION: Find the point at which the line intersects the given plane. Line: 5x= y/2= z+2. Plane: 10x-7y+3z+24=0

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Question 1049400: Find the point at which the line intersects the given plane.
Line: 5x= y/2= z+2.
Plane: 10x-7y+3z+24=0
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
At that point,
5x=y%2F2<--->y=10x ,
5x=z%2B2<--->z=5x-2 , and
10x-7y%2B3z%2B24=0 .
That is a system of linear equations.
You can easily solve it by substitution.
Substituting 10x for y , and 5x-2 for z in the long equation, you get
10x-7%2810x%29%2B3%285x-2%29%2B24=0
20x-70x%2B25x-6%2B24=0
-45x%2B18=0
18=45x
x=18%2F45
highlight%28x=2%2F5%29 .
Then y=20%282%2F5%29 , so highlight%28y=4%29 , and
z=5%2A%282%2F5%29-2 , so z=2-2, and highlight%28z=0%29 .
You can say that the point where the line crosses the plane is (2/5,4,0) .