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## Graphing Method To Solve System Of Linear Equations

**Systems of Linear Equations – Solving by Graphing**

The graphing method is one of the methods for solving systems of linear equations. When there are two equations in two variables, both equations are drawn on the coordinate grid and the point of intersection is the solution of the given equations.

A system of equations in degree one is called linear because a degree one equation, when drawn on a grid, always forms a straight line. The graph of a degree one equation gives a straight line, so equations in “degree one” 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 drawn on the coordinate frame. When both lines are drawn on the graph, a point of intersection exists, which gives the values of both variables and hence the solution of the given equations.

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

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

2. **Interrupt method:** A second method of graphing a given equation is to find the intercepts of both lines. Once both intercepts (x-intercept and y-intercept) have been calculated for both lines, they are drawn in the coordinate frame. The next process is the same as in the table method above. The intersection point 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 line. Once the slopes of both lines are 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 slope is divided by the run, in other words, the slope fraction indicates movement from the y -intercept up to the bottom and the slope denominator indicates movement from left to right. For example; If the slope is 2/3, that means 2 points up and 3 points to the right from y – the intercept to find the next point and so on.

Finally, to solve a system of linear equations graphically, students can adopt one of three approaches; Table method, intercept method and slope, y-intercept method.

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