System of linear equations
October 13, 2019 post by kiennt

A system of linear equations means two or more linear equations. If two linear equations intersect, that point of intersection is called the solution to the system of equations.

1. The system has exactly one solution: When two lines have different slope, the system has only one solution
2. The system has no solution: When two lines are parallel and have different y-intercept, the system has no solution.
3. The system has infinitely many solutions: When two lines are parallel and the lines have the same y-intercept.

From the standard form for the system of equations.

$$a_{1}x+b_{1}y=c_{1}$$ $$a_{2}x+b_{2}y=c_{2}$$