document.write( "Question 1049400: Find the point at which the line intersects the given plane.
\n" ); document.write( "Line: 5x= y/2= z+2.
\n" ); document.write( "Plane: 10x-7y+3z+24=0 \n" ); document.write( "

Algebra.Com's Answer #665050 by KMST(5328) $\"\"$ $\"About$

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At that point,
\n" ); document.write( " $\"5x=y%2F2\"$ <---> $\"y=10x\"$ ,
\n" ); document.write( " $\"5x=z%2B2\"$ <---> $\"z=5x-2\"$ , and
\n" ); document.write( " $\"10x-7y%2B3z%2B24=0\"$ .
\n" ); document.write( "That is a system of linear equations.
\n" ); document.write( "You can easily solve it by substitution.
\n" ); document.write( "Substituting $\"10x\"$ for $\"y\"$ , and $\"5x-2\"$ for $\"z\"$ in the long equation, you get
\n" ); document.write( " $\"10x-7%2810x%29%2B3%285x-2%29%2B24=0\"$
\n" ); document.write( " $\"20x-70x%2B25x-6%2B24=0\"$
\n" ); document.write( " $\"-45x%2B18=0\"$
\n" ); document.write( " $\"18=45x\"$
\n" ); document.write( " $\"x=18%2F45\"$
\n" ); document.write( " $\"highlight%28x=2%2F5%29\"$ .
\n" ); document.write( "Then $\"y=20%282%2F5%29\"$ , so $\"highlight%28y=4%29\"$ , and
\n" ); document.write( " $\"z=5%2A%282%2F5%29-2\"$ , so $\"z=2-2\"$ , and $\"highlight%28z=0%29\"$ .
\n" ); document.write( "You can say that the point where the line crosses the plane is (2/5,4,0) . \n" ); document.write( "

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