Find the intersection of the planes. -9x - 8y - 8z = 74 and 8x - 5y + 3z = -21
A) x = -2 - 16t, y = -2 + 91t, z = -5 + 19t
B) x = 16t, y = -91t, z = -19t
C) x = -2 - 64t, y = -2 - 37t, z = -5 + 109t
D) The planes are parallel.

Question

Quizplus · Accepted Answer

We can solve for x, y, and z by setting up a system of equations:
-9x - 8y - 8z = 74
8x - 5y + 3z = -21
Multiplying the second equation by 9/8, we get:
9x - (45/8)y + (27/8)z = -47.25
Adding this to the first equation, we get:
(1/8)x - (49/8)y - (49/8)z = 26.75
Solving for x, y, and z using this equation and the second equation, we get:
x = -2 - 64t
y = -2 - 37t
z = -5 + 109t
Therefore, the intersection of the planes is given by choice C.

Find the Intersection of the Planes