Describe how to determine the number of solutions that a system of equations has (one, none, or infinite).

Question

Describe how to determine the number of solutions that a system of equations has (one, none, or infinite).

Answer 1

x+y = 2

2x +2y = 4 has an infinite number of solutions. They're the same line graphically, and coincide in every point. They are linearly dependent. You can derive one equation from the other, by multiplying b 2

x+y = 2

x+y = 4 has zero solutions. They are parallel lines that never intersect

x+y=2

2x+y=2 has one unique solution. (0,2) the y intercept graphically of both equations. They intersect at (0,2)