How To Solve A Quadratic Equation By Quadratic Formula Graphing Method To Solve System Of Linear Equations

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Graphing Method To Solve System Of Linear Equations

A System of Boundary Relations – Solved by Programming

The graph method is one of the ways to solve a system of linear equations. When there are two equations in two variables, both equations are drawn on the coordinate grid and the intersection becomes the solution of the given equations.

A system of first degree equations is called a line because first degree equations, when drawn on a grid, always form a straight line. Since the graph of degree one equations gives a straight line, that is why equations in degree one are called linear equations.

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

1. Table Method: This way students can substitute the value of one variable into an equation and get the corresponding value of the other variable. This set of two values ​​is called a point. The process is repeated to obtain three to five points. Then all the points are plotted on the coordinate frame. When both lines are drawn on the graph, the point of intersection is found, which gives the value of both variables and thus the solution of the given equations.

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

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

2. How to Prevent: A second way to graph the given equations is to find the intercepts on both lines. Once both intercepts (x – intercept and y – intercept) of both lines are calculated, they are plotted on the coordinate frame. The additional process is similar to the table method above. The intersection point gives the solution to the equations.

3. Slope and y-intercept: To use this method, students should be familiar with how to find the slope of a line. There is a special formula for finding the slope of a line. After 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 the line.

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

Finally, to solve a system of linear equations graphically, students can take one of these three methods; Tabular path, intercept and slope, y -intercept.

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