Graphically, the solution to a system of two independent linear equations is usually what?

Linear equations are one of the most integral parts of mathematics and are used to solve a lot of problems in various fields. They are represented as straight lines on the cartesian plane. We can solve these equations by various methods; one of them is the graphical method. Let's have a deeper look into this concept.

Answer: Graphically, the solution to a system of two independent linear equations is usually the point where the graphs of both the equations are intersecting or in some cases, overlapping.

Let's understand the problem in detail.

Explanation:

A system of two independent linear equations can be represented in the graph using straight lines.

These systems can fall into any of the below three categories:

• A system of two independent linear equations that have only one solution: This type of system can have only one unique solution, that is, the point where both the straight lines are intersecting.
• A system of two independent linear equations that have infinitely many solutions: This type of system can have infinitely many solutions. The graphs of both the equation overlap each other in this case.
• A system of two independent linear equations that have no solution: This type of system has no solutions. The graphs never intersect and are parallel to each other in this case.

Hence, graphically, the solution to a system of two independent linear equations is usually the point where the graphs of both the equations are intersecting or in some cases, overlapping.