Analysis from graph -III

Given below is a graph representing pair of linear equations in two variables x-y=2 , x+y=4 Answer the following questions:

1. What are the coordinates of points where two lines meet x-axis?


2. What are the coordinates of points where two lines meet y-axis?


3. What is the solution of given pair of equations? Read from graph.


4. What is the area of triangle formed by given lines and x-axis?


5. What is the area of triangle formed by given lines and x-axis?
   

Analysis from graph -II

Given below is the graph representing pair of linear equations in two variables
x-y=4 ,x-2y=4

The given two lines intersect at (4,0) which is the solution of given pair of linear equations in two variables.
Coordinates of points where lines cut the y-axis are A (0,-4) and C(0,-2)
Vertices of triangle formed by given lines and y-axis are A(0,-4), B(4,0) and C(0,-2)
The area of triangle ABC = 1/2 (2 x 4) = 4 square units

Analysis from graph -I

Given below is a graph representing pair of linear equations in two variables.
x+y=4 , 3x-2y=12
Observe the following carefully...

• The given two lines intersect at (4,0) which is the solution of given pair of linear equations in two variables.
• Coordinates of points where lines cut they-axis are A (0,4) and C(0,-6)
• Vertices of triangle formed by given lines and y-axis are A(0,4), B(4,0) and C(0,-6)
• The area of triangle ABC = 1/2 (10 x 4) = 20 square units
  

Assignment-Activity 3

Answer the following questions after doing activity 3.
Q1 Write the condition for having no solution in the following pair of linear equations in two variables lx +my= p and tx+ny=r .

Q2 Without actually drawing graph can you comment on type of graph of a given pair of linear equations in two variables?

Q3 If ratio of coefficients of x is equal to ratio of coefficients of y and not equal to ratio of constant terms in a given pair of linear equations in two variables then what will be the type of graph?

Q4 Write 2 more equations of lines parallel with 3x+7y=9 .

Q5 Comment on type of solution and type of graph of following pair of linear equations:
3x-5y=11 , 6x-10y=7

Q6 For what value of K the pair of equations Kx+2y=5 , 3x-4y = 10 has no solution.

Q7 Comment on the consistency or inconsistency of a pair of linear equations in two variables having parallel lines on graph.

Q8 Find the value of K for which the pair of equations 3x+y = 1 , (2K-1 )x + (K-1)y = (2K+1)
has no solution.

Assignment-Activity 2

Answer the following questions after doing activity 2.

Q1 Write the condition for having infinitely many solution in the following pair of linear equations in two variables lx +my= p and tx+ny=r .

Q2 Without actually drawing graph can you comment on type of graph of a given pair of linear equations in two variables?

Q3 If ratio of coefficients of x is equal to ratio of coefficients of y and also equal to ratio of constant terms in a given pair of linear equations in two variables then what will be the type of graph?

Q4 Write 2 more equations of lines coincident with 5x+7y=20 .

Q5 Comment on type of solution and type of graph of following pair of linear equations:
2x-5y=9 , 4x-10y=18

Q6 For what value of k the pair of equations x+(k+1) y = 5 , (k+1)x +9y = 8k-1 has infinitely many solutions.

Q7 Comment on the consistency or inconsistency of a pair of linear equations in two variables having coincident lines on graph.

Q8 Find the value of k for which the pair of equations 2x+3y=7 , (k-1)x + (k+2) y = 3k has infinitely many solutions

Assignment -Activity 1

Answer the following questions after doing activity 1

Q1 Write the condition for having a unique solution in the following pair of linear equations in two variables lx +my= p and tx+ny=r .

Q2 Without actually drawing graph can you comment on type of graph of a given pair of linear equations in two variables?

Q3 If ratio of coefficients of x is not equal to ratio of coefficients of y in a given pair of linear equations in two variables then what will be the type of graph?

Q4 Write 2 more equations of lines intersecting with 3x+7y=9 .

Q5 Comment on type of solution and type of graph of following pair of linear equations
2x-5y=9
5x+6y=8

Q6 For what value of K the pair of equations x-2y=3 , 3x+Ky = 1 has a unique solution.

Q7 Comment on the consistency or inconsistency of a pair of linear equations in two variables having intersecting lines on graph.

Q8 Find the value of K for which the pair of equations x+2y=3 , 5x+ky+7=0 has a unique solution.