Graphing equations in order to identify a specific point of intersection is usually not a precise way to solve systems because it is often difficult to see exactly where two lines intersect (unless you are using a computer-based graphing program that allows you to zoom in on a point).

Graphing is not always the best method for solving a system of equations. For example, if you graph the system below, you get the following graph. While you can approximate the solution to this system, you cannot say exactly where the intersection point is since it does not fall on integer values on the number lines.

Linear equations use one or more variables where one variable is dependent on the other. Solving Systems Of Equations Using Linear Combinations. Disadvantages of solving system of linear equations by graphing are: The point of intersection may not be accurate as some may have decimal solutions.

The advantage of solving a system of linear equations by graphing is that it is relatively easy to do and requires very little algebra, and the main disadvantage is that your answer will be approximate due to having to read the answer from a graph.

Elimination has less steps than substitution. Elimination reduces the possibilities of mistakes as compared to other methods. Elimination is quicker.

If equation is already in the form of one variable expressed (or easily expressible) in terms of another variable, substitution is faster. On the other hand, if coefficient of one variable is same (or can be made same by multiplication) in both the equations, elimination can produce result faster.

The elimination method is one of the most widely used techniques for solving systems of equations. Why? Because it enables us to eliminate or get rid of one of the variables, so we can solve a more simplified equation.

Because this system has at least one solution it is considered to be consistent. Consistent systems are systems which have at least one solution. If the system has exactly one, unique solution then it is independent. If the system has infinite solutions, then it is called dependent.

consistent independent system

The solution to a system of linear equations is the point at which the lines representing the linear equations intersect. Two lines in the x y xy xy -plane can intersect once, never intersect, or completely overlap.

Add (or subtract) a multiple of one equation to (or from) the other equation, in such a way that either the x -terms or the y -terms cancel out. Then solve for x (or y , whichever’s left) and substitute back to get the other coordinate. Multiply the first equation by −2 and add the result to the second equation.