Shade the region bounded by these lines and also y-axis. (iii) Another coincident line to above line isĮxample 10: Solve the following system of linear equations graphically (ii) Another parallel lines to above line is (i) Another linear equation in two variables such that the geometrical representation of the pair so formed is intersecting lines is Geometrical representing of the pair so formed is : Hence, the given system of equations has no solution.Įxample 9: Given the linear equation 2x + 3y – 8 = 0, write another linear equation in two variables such that the As they have no common point, there is no common solution. Similarly, plot the points C(–3, 4), D(3, 0) and join them to get a line CD.Ĭlearly, the graphs of the given equations are parallel lines. Plot the points A (–4, 6), B(2, 2) and join them to form a line AB. (x – 7) = 7(y – 7) or x – 7y = – 42 ….(1)Īfter 3 years father’s age = (x + 3) yearsĪfter 3 years daughter’s age = (y + 3) yearsĪccording to the condition given in the question Seven years ago daughter’s age = (y – 7) years Seven years ago father’s age = (x – 7) years Let the present age of father be x years and that of daughter = y years Also, three years from now, I shall be three times as old as you will be.” Represent this situation algebraically and graphically. Every point on CD gives us a solution of equation (2).Įxample 2: A father tells his daughter, “ Seven years ago, I was seven times as old as you were then. Now, every point on the line AB gives us a solution of equation (1). Clearly, the two lines intersect at the point C. Plot the points A (1, 6), B(4, 3) and join them to form a line AB. Hence, the equations are inconsistent.įrom the table above you can observe that if the line a 1x + b 1y + c 1 = 0 and a 2x + b 2y + c 2 = 0 areĮxample 1: The path of highway number 1 is given by the equation x + y = 7 and the highway number 2 is given by the equation 5x + 2y = 20. The graphs (lines) of the given equations are parallel.
![finding solutions for 3 equation systems with 2 variables finding solutions for 3 equation systems with 2 variables](http://i.ytimg.com/vi/cGC9sBRYq-A/maxresdefault.jpg)
![finding solutions for 3 equation systems with 2 variables finding solutions for 3 equation systems with 2 variables](https://i.ytimg.com/vi/3_M1GI1erWo/maxresdefault.jpg)
No Solution: The graph (lines) of the two equations are parallel. (B) Inconsistent Equation: If a system of simultaneous linear equations has no solution, then the system is said to be inconsistent. Hence, the given equations are consistent with infinitely many solutions. Coordinates of every point on the lines are the solutions of the equations. The graphs of the above equations coincide. (ii) Consistent equations with infinitely many solutions: The graphs (lines) of the two equations will be coincident.įor Example Consider 2x + 4y = 9 ⇒ 3x + 6y = 27/2 Hence, the equations are consistent with unique solution. The graphs (lines) of these equations intersect each other at the point (2, 1) i.e., x = 2, y = 1.
![finding solutions for 3 equation systems with 2 variables finding solutions for 3 equation systems with 2 variables](https://image.slidesharecdn.com/pairoflinearequationintwovariable-131029112326-phpapp01/95/pair-of-linear-equation-in-two-variable-6-638.jpg)
(i) Consistent equations with unique solution: The graphs of two equations intersect at a unique point. (A) Consistent: If a system of simultaneous linear equations has at least one solution then the system is said to be consistent.
![finding solutions for 3 equation systems with 2 variables finding solutions for 3 equation systems with 2 variables](https://i.ytimg.com/vi/suQrupzFS74/maxresdefault.jpg)
Graphical Method Of Solving Linear Equations In Two Variables