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## Graphing Method To Solve System Of Linear Equations

**System of linear equations – Solve using graphs**

The graphical method is one of the methods to solve the system of linear equations. When there are two equations in two variables, the two equations are plotted on the coordinate grid and the point of intersection becomes the solution of the given equations.

The system of degree 1 equations is called linear because the degree 1 equations, when plotted on the grid, always form a straight line. Since the graph of the equation of degree 1 gives a straight line, that is why equations of “degree 1” 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 graph the given lines.

1. **Tabular method: **In this method students can substitute the value of one variable into the 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. Then all the points are plotted in the coordinate frame. When the two lines are drawn on the graph, the point of intersection is located, which gives the value of the two variables and thus the solution of the given equations.

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

If the two lines overlap, this means that there are infinitely many points of intersection between the lines, and therefore infinitely many solutions to the system of equations.

2. **Interception method:** The second method of graphing the given equations is to find the intercepts of the two lines. Once the two intercepts (x – intercept and y – intercept) of the two lines are calculated, they are plotted in the coordinate frame. The subsequent procedure is the same as in the tabular method above. The point of intersection gives the solution to the equations.

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

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

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

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