For a linear system with two variables and two equations, we can determine the type of solutions without computation by examining the slopes and y-intercepts of the lines represented by the equations.
For a linear system with two variables and two equations, we can say the following about its solutions:
If the system has one unique solution, it means the two lines represented by the equations intersect at a single point.
If the system has no solution, it means the two lines are parallel and will never intersect.
If the system has infinite solutions, it means the two lines are coincident, meaning they are the same line and intersect at all points.
These conclusions can be justified without any computation by examining the slopes and y-intercepts of the lines represented by the equations and determining their relationship.