Find the point of intersection between a sphere and a plane

[Chef G]

I have a plane equation given by 3x-2y+z=0
and a sphere given by (x-1)^2+(y-1)^2+(z-1)^2=(2sqrt(14))/7.
The question asks to find the point of intersection between the two using those equations as a system of equations with x and y as the two unknowns. I really appreciate any help!

 

[Dr.Peterson]

I have a plane equation given by 3x-2y+z=0
and a sphere given by (x-1)^2+(y-1)^2+(z-1)^2=(2sqrt(14))/7.
The question asks to find the point of intersection between the two using those equations as a system of equations with x and y as the two unknowns. I really appreciate any help!

That's very odd.

A plane and a sphere typically intersect in a circle, not a point; and the equations have three unknowns, not just two. So it seems they are saying to take z as fixed, in effect asking for the intersection of the plane and the sphere and a third plane, z=k. But that would typically result in two points, not just one.

Please quote the entire problem exactly as given to you, so we can be sure we understand it.