Graphing System of Equations

Graphing system of equations is useful to represent the equations of lines or curves in the two-dimensional coordinate system and to easily learn the various features of the represented graph. The point of intersection of the lines, the intercepts made with respect to the coordinate axis, the area enclosed by the lines, can all be studied by graphing system of equations.

Let us learn more about the graphing system of linear equations, inequations, how to graph system of equations, advantages of graphing system of equations, with the help of examples, FAQs.

Graphing system of equations helps in knowing the point of intersection of the lines, the area enclosed by the equation lines, and the intercepts made by the lines with respect to the coordinate system. For the graphing system of equations, the equations can include for a line or a curve. Here we consider the lines for graphing system of equations. The simplest form of an equation for graphing is the standard form of the equation of a line, which is ax + by + c = 0.

Here we consider the graph of the equations a₁x + b₁y + c₁ = 0, and a₂x + b₂y + c₂ = 0, and aim at finding the point of intersection, intercepts made by the lines, the relationship between the lines, and the area enclosed by the lines.

The simplest form of linear equations is the equation of lines parallel to the coordinate axis. The line x = a is a line parallel to the y-axis, and the line y = b is a line parallel to the x-axis, and both these equations represent a system of equations that intersect at the point (a, b), and these systems of equations make a rectangle with the coordinate axis, whose area is ab square units.

This is the simplest form of linear equations and we can find the x-intercept and y-intercepts made by the lines. The line x = a , cuts the x-axis at the point (a, 0), and makes an intercept of a units on the x-axis, and the line y = b cuts the y-axis at the point (0, b) and makes intercepts of b units on the y-axis.

The graphing of the system of inequations helps in knowing the range of values of the equations. First, assume the inequations as equations and aim at drawing the graph of the equations. Further, on drawing the system of linear equations we need to convert it into inequations by replacing the lines with the dotted lines. Further, we need to select a random point on either side of the lines to check if it satisfies the inequality sign, and shade the region which satisfies the inequality sign.

Here we consider the graphs of the inequalities a₁x + b₁y + c₁ > 0, and a₂x + b₂y + c₂ < 0, and represent the above graph. The dotted line is made into a simple straight line, if the inequalities > or < are changed to > or <.

The graphing system of equations requires us to follow the below sequence of steps.

• First, identify two points on the line which can be plotted to draw the line.
• Identifying two points is possible by writing x = 0 to get the y-intercept or a point on the y-axis, and by writing y = 0 we can get the x-intercept or a point on the x-axis.
• Join the points on both axes to get the required graph of the straight line.
• Similarly draw the graph of the other straight line, with the help of any two points on the line.

Thus the graph of the system of equations has been drawn. This graph helps in knowing the orientation of the lines and to know if the two lines are intersecting or not.

The graphing system of equations helps in the following aspects.

• Point Of Intersection: The point of intersection of the equation representing the lines or curves can be easily identified with the help of graphing of the system of equations.
• Orientation Of Lines: The inclination of the lines with reference to the coordinate axis can be found by the graphing system of equations
• Relation Between The Lines: The graphing of the system of equations helps in knowing if the two lines are intersecting lines, parallel lines, or coincident lines.
• Intercepts Made by the Lines: The intercepts made by the lines can be found by knowing the points on the coordinate axis where the graph lines cut the x-axis and the y-axis.
• Area Enclosed by the Lines: The area enclosed by a line or a pair of lines can be computed by graphing the system of equations. The use of integration and with the application of limits help in finding the values of

☛ Related Topics

• Graphing Functions
• Graphing Quadratic Functions
• Graphing Complex Numbers
• Introduction to Graphing
• Graphing Calculator

What Is Graphing System of Equations In Algebra?

The graphing of system of equations is helpful to represent the linear one-degree algebraic expression as a line, and then perform numerously geometric analysis. The plotting of lines is helpful to find the point of intersection, the relation between the lines, the intercepts made by the lines, and the area enclosed by the lines.

How To Graph System of Equations?

The graphing system of equations is possible by knowing any two points on the line. For graphing a line having an equation ax + by + c = 0, we can identify two simple points by first substituting x = 0 to get the point (0, -c/b), and then substitute y = 0 to get the point (-c/a, 0).

What Is Required For Graphing System Of Linear Equations?

The minimum required thing for graphing the system of linear equations is any two points on the line. The two points on the line ax + by + c = 0 can be plotted in the coordinate system and then the line passing through these two points can be plotted to get the required graph for the line.

What Are The Steps For Graphing System Of Linear Equations?

The following sequence of steps is helpful for graphing system of linear equations.

• First, identify any two points on the line.
• Plot the points, and join the two points to get the required line.
• Plot other lines also to get the point of intersection of the lines.

How To Solve System of Equations By Graphing?

The system of equations can be solved by graphing the system of equations and finding the point of intersection of the lines. These point of intersection is the solution of these lines, and is also the points where these lines intercept the coordinate axis.