Flashcard 7 - Mathematics: Algebraic Reasoning Flashcard Set for the TSIA2

no solution, unique solution, and infinite solutions

When two lines are parallel to each other, the system has no solution and there is no intersection point:

\(y = 2x + 4\) and \(y = 2x + 10\)

When two lines intersect at one point, the intersecting point is the unique solution of the system:

\(y - 2x = 5\) and \(3x - y = 5\)

When two equations of a linear system are essentially the same line (constant multiple of each other), we have infinitely many solutions:

\(-4x+y = 2\) and \(-12x + 3y = 6\)