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 formax1 + 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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