Mathematics Lab Activity-02 Class 10 | Linear Equations

   Mathematics Lab Activity-02 Class X

Mathematics Laboratory Activities on Pair of linear equations in two variables for class X students with complete observation tables strictly according to the CBSE syllabus.

Chapter - 03 

pair of linear equations

Activity - 02

OBJECTIVe

To verify the conditions of consistency/ inconsistency for a pair of linear equations in two variables by graphical method.

MATERIAL REQUIRED

Graph papers, pencil, eraser, cardboard, glue.

Procedure

1. Take a pair of linear equations in two variables of the form

ax₁ + by₁ + c₁ = 0  ….. (i)

ax₂ + by₂ + c₂ = 0  ….. (ii) 

There may be three cases :

2. Case I :     or         

Students may take the example of the lines as:  -2 x + 4 y = 7,   4 x + 5 y = 9

3. Obtain the ordered pairs satisfying the pair of linear equations (1) and (2) for each of the above cases.

4. Take a cardboard of a convenient size and paste a graph paper on it. Draw two perpendicular lines X′OX and YOY′ on the graph paper (see Fig. 1).

5. Plot the points obtained in step 3 in the cartesian plane to obtain the two intersecting lines as shown in the figure 1

Figure 1

6. Case II :  

Students may take the example of the lines as: 2x - 4y = 7, 4x - 8y = 14

7. Obtain the ordered pairs satisfying the pair of linear equations (1) and (2) for each of the above cases.

8. Take a cardboard of a convenient size and paste a graph paper on it. Draw two perpendicular lines X′OX and YOY′ on the graph paper (see Fig. 2).

9. Plot the points obtained in step 7 in the cartesian plane to obtain the two intersecting lines as shown in the figure 2

Figure 2

10. Case III :   

Students may take the example of the lines as:  2x - 4y = 7,  2x - 4y = - 5

11. Obtain the ordered pairs satisfying the pair of linear equations (1) and (2) for each of the above cases.

12. Take a cardboard of a convenient size and paste a graph paper on it. Draw two perpendicular lines X′OX and YOY′ on the graph paper (see Fig. 3).

13. Plot the points obtained in step 11 in the cartesian plane to obtain the two intersecting lines as shown in the figure 3

Figure 3

Observations

Case I: We obtain the graph as shown in Fig. 1. The two lines are intersecting at one point P. Co-ordinates of the point P (x,y) give the unique solution for the pair of linear equations (1) and (2).

Therefore, the pair of linear equations with   is consistent and has the unique solution.

Case II: We obtain the graph as shown in Fig. 2. The two lines are coincident. Thus, the pair of linear equations has infinitely many solutions.

Therefore, the pair of linear equations with   is also consistent as well as dependent.

Case III: We obtain the graph as shown in Fig. 3. The two lines are parallel to each other.

This pair of equations has no solution, i.e., the pair of equations with   is inconsistent.

OBSERVATION TABLE

Conditions	Nature of Solution	Type of Graph	Consistent /Inconsistent
	Unique Solution	Two intersecting lines	Consistent
	Unique Solution	Two intersecting lines	Consistent
	Infinitely many solutions	Coincident lines	Consistent
	No Solution	Two Parallel Lines	Inconsistent

Result

(i) If graph is two intersecting lines then the given system of linear equations are consistent.

(ii) If graph is two coincident lines then the given system of linear equations are consistent.

(iii) If graph is two Parallel lines then the given system of linear equations are inconsistent.

APPLICATION

Conditions of consistency help to check whether a pair of linear equations have solution (s) or not.

In case, solutions/solution exist/exists, to find whether the solution is unique or the solutions are infinitely many.

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