Question

Tell how many solutions there are for a system of linear equations whose graph is described below. Be sure to explain/justify your answer. (3 pts.)

a. A pair of parallel lines
a.
b. A single line

c. A pair of lines that are not parallel

Answer 1

if by "solutions" they mean points where they exist then all three are infinity. if they mean solutions as in intersecting points then A has none, B has none and C would be the corssing point of the two lines

Answer 2

Ya I didn't really know what they meant, but thanks

Answer 3

Solutions to systems of equations are points which all equations have in common.

So two parallel lines have no points in common (they never cross).

A single line has only one equation and would thus have infinitely many solutions. Because it would have all it's points in common with itself.

A pair of non-parallel lines would have only one solution because two non-parallel lines can only intersect at a single point.