SOLUTION: Show that the following lines intersect. Find the coordinates of the point of intersection and the angle of intersection. L1: x=7+2t y=4+t and L2: x=-

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Question 1036413: Show that the following lines intersect. Find the coordinates of the point of intersection and the angle of intersection.
L1: x=7+2t
y=4+t
and
L2: x=-3+3s
y=4-s
Thanks sooo much :)
Found 2 solutions by Aldorozos, ikleyn:
Answer by Aldorozos(172) (Show Source):
You can put this solution on YOUR website!
We have to get rid of t
X=7+2t
Y= 4+ t therefore t= y-4
Substituting t in the first equation we get x= 7+2(y-4)
Therefore x= 2y-1

Now we do the same with the second equation by eliminating s
X= -3 +3(4-y)
Therefore x=9-y
Now from the first equation we have x=2y-1
And from the second equation we have x=9-y
Since both are equal to x therefore both sides have to be equal which means 2y-1= 9-y
Solving this equation gives us y=10. If y=10 and x=9-y then x= -1 the point x=-1 and y=10 is the intersection. Since we find the point, this means the lines are not parallel and they intersect.

Answer by ikleyn(52788) (Show Source):
You can put this solution on YOUR website!
.
Below please find my corrections to the solution of the previous tutor.
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. . .
Since both are equal to x therefore both sides have to be equal which means 2y-1= 9-y.

Solving this equation gives us 3y=10, and then y = = .

If y = and x=9-y then x= .

The point (x,y) = ( , ) is the intersection.

Since we found the point, this means the lines are not parallel and they intersect.