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## Graphing Method To Solve System Of Linear Equations

**System of Linear Equations – Solve by graphing**

The graphical method is one of the methods for solving a system of linear equations. If there are two equations in two variables, both equations are plotted on the coordinate grid and the intersection point becomes the solution of the given equations.

A system of equations of the first degree is called linear because the equations of the first degree always form a straight line when drawn on a grid. Since the graph of an equation of the first degree gives a straight line, “degree 1” equations are called linear equations.

To solve two equations in two variables using the graphing method, students can use one of the following three methods to draw the given lines.

1. **Table method: **In this method, students can substitute the value of one variable into an equation and find the corresponding value of the other variable. This set of two values is called a point. The process is repeated to find three to five points. All points are then plotted on the coordinate frame. If both straight lines are drawn on the graph, the point of intersection is located, which gives the value of both variables and, consequently, the solution of the given equations.

If both lines are parallel to each other, then there is no point of intersection between the lines, so there is no solution to the given system of linear equations.

If both lines overlap, which means that there are an infinite number of points of intersection between the lines, and thus the system of equations has an infinite number of solutions.

2. **Termination method:** Another method of graphing the given equations is to find the points of intersection of both lines. Once the points of intersection of both lines (x-intercept and y-intercept) have been calculated, they are plotted on the coordinate frame. The further procedure is the same as the above tabular method. The intersection gives the solution to the equations.

3. **Slope and y-intercept method: **To use this method, students should be familiar with finding the slope of a line. There is a special formula for finding the slope of a line. Once the slopes of both lines have been found, the y-intercepts of the lines are calculated. In this case, starting from the y -intercept, the slope is used to move along the line.

Students should know that the rise is divided by the run, in other words the numerator of the slope shows movement from top to bottom from the y-intercept and the denominator of the slope shows movement from left to right. For example; if the slope is 2/3, that means 2 points up and 3 points directly from y – the intercept to find the next point, and so on.

Finally, students can use one of three approaches to solve a system of linear equations graphically; table method, intercept method and slope, y – intercept method.

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