Question

Graph each system. Tell whether the system has no solution, one solution, or infinitely many solutions.

Answer 1

Answer: Infinitely many solutions

The second equation is equivalent to y = 2x - 5 when we subtract 5 from both sides, but this is the exact same as the first equation given to us. So we effectively have 2 copies of the same thing. One is just written in a different format.

Graphing these equations leads to the straight line. One line will be right on top of the other one. The two lines intersect an infinite number of times leading to infinitely many solutions. Any solution point is simply a point on the line y = 2x-5. The solution ordered pair is of the form (x,y) = (x, 2x-5). Two example points on this line are (0,-5) and (1,-3)

side note: We can say that this system is consistent (because it has at least one solution) and it's also dependent (because one equation depends on the other; or it is basically a copy)