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We have because. Hence, lines have unique solution which means they intersect at one point. We get,. Here which means equations have unique solution. Here because. We get, , ,. We can see that both of the lines coincide. Hence, there are infinite many solutions. Any point which lies on one line also lies on the other. We can assume any random values for y and can find the corresponding value of x using the above equation. Thus, the graphs of the two equations are coincident.
Consequently, every solution of one equation is a solution the other. Hence, the system of equations has infinitely Ncert Solutions Of Class 10th Exercise 3.2 Ed many solutions, i. Plotting the points A 0, � 8 and B 8, 0 on a graph paper. So, the two lines have no common point. Hence, the given equations has no solution, i. Clearly, the two lines intersect at point P 2, 2. Plot the points A 2, 0 and B 0, �2 on a graph paper. We find the graphs of these equations are parallel lines.
The common point on both the lines, there is one and only one solution for the pair of linear equations in two variables. Parallel lines never intersect each other. So, there is no solutions for these system of linear equations. If the lines are coincident, then every point on the line is the solutions for the equations. There are infinitely many solutions. Class 10 Maths Exercise 3. Class 10 Maths Chapter 3 Exercise 3.
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