Graphical Method of Solution of a Pair of Linear Equations

The graphical method can be imprecise when finding exact values, especially if the point of intersection is not on grid lines. It also becomes less practical when dealing with more complex systems or when precise solutions are required.

Yes, by comparing the ratios of the coefficients a₁/a₂, b₁/b₂, and c₁/c₂, we can determine the type of solution:If a₁/a₂ ≠ b₁/b₂, the lines intersect and there is a unique solution. If a₁/a₂ = b₁/b₂ = c₁/c₂, the lines are coincident and there are infinitely many solutions. If a₁/a₂ = b₁/b₂ ≠ c₁/c₂, the lines are parallel and there is no solution.

If the equations have different slopes, it means the lines will intersect at a single point. Therefore, the system of equations will have a unique solution.

Infinitely many solutions occur when the two lines overlap completely, or in other words, they are coincident. This means every point on the line satisfies both equations, so there are infinitely many solutions.

A unique solution exists when the lines represented by the equations intersect at exactly one point. This means there is one specific pair of values for x and y that satisfies both equations.

If two lines are parallel, it means that they will never intersect, indicating that there is no common solution to the equations. In this case, the equations are said to be an "inconsistent pair" and have no solution.

In the graphical method, the point of intersection represents the solution to the pair of equations. The coordinates (x, y) of the intersection point satisfy both equations simultaneously.

The graphical method involves plotting each equation on a graph as a line and finding the point(s) of intersection. The coordinates of the intersection point represent the solution to the equations. If the lines intersect at a single point, there is a unique solution. If they are parallel, there is no solution, and if they coincide, there are infinitely many solutions.