Yes. If two planes are not coincident (the same plane) and are not parallel,
then they intersect in one straight line.
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Yes.
If it is a linear system, then it could have either 1 solution, no solutions, or infinite solutions. To understand this, think of two lines (consider a plane which is just 2 dimensional - this represents 2 variables and 2 equations, but the idea can be extended to more dimensions).If the 2 lines intersect at a point, then that point represents a solution. If the lines are parallel, then they never intersect, and there is no solution. If the equations are such that they are just different ways of describing the same line, then they intersect at every point, so there are infinite solutions. If you have more than 2 lines then maybe some of them will intersect, but this is not a solution for the whole system. If all lines intersect at a single point, then that is the single solution for the whole system.If you have equations that describe something other than a straight line, then it's possible that they may intersect in more than one point.
If the lines are straight lines , then there is only one solution, which is the point of intersection of the two lines. It will have ( x,y) coordinates. However, if the lines are curved in any way , there may be more than two or more points of intersection.
It is incorrect to say that sphere has lateral area. First sphere do not have sides like other geometric figure. In fact a line or plane can intersect the surface of a sphere in just one point. Sphere has no lateral side. It is enough to say surface area of sphere than lateral surface area of the sphere.
A frustrum of a cone, A sphere intersected by two planes, An ellisoid intersected by two planes, A torus (doughnut) with a radial slice removed, A torus intersected by a plane nearer than its inner radius, A cylinder, and many more.