Question

How many solutions would a system of three linear equations in three variables have if it could be graphed by two overlapping planes intersected by a third plane?(1 point)
Responses

infinite number of solutions
infinite number of solutions

one solution
one solution

two solutions
two solutions

no solutions

Answer 1

If a system of three linear equations in three variables is graphed such that two of the equations represent overlapping planes and the third plane intersects them, the system will have **infinite number of solutions**. This is because the two overlapping planes coincide, providing a common two-dimensional plane of intersection, while the third plane can intersect it in a line, leading to an infinite number of solutions along that line.

So the correct answer is:
**infinite number of solutions**.