NCERT solutions for class 10 maths chapter 3 part 4

In this page NCERT solutions for class 10 maths chapter 3 part 4 you can find solutions for exercise problems.

NCERT solutions for class 10 maths chapter 3 part 4

(4) Which of the following pairs of linear equations are consistent/inconsistent? if consistent,obtain the solution graphically:

(i)  x + y = 5

   2 x + 2 y = 10

Solution:

    x + y - 5 = 0

   2 x + 2 y - 10= 0

From the above information let us take the values of a₁, a₂, b₁, b₂, c₁ and c₂

 a₁ = 1          b₁ = 1            c₁ = -5

 a₂ = 2         b₂ = 2            c₂ = -10

a₁/a₂ = 1/2

b₁/b₂ = 1/2

c₁/c₂ = -5/-10 = 1/2

This exactly matches the condition a₁/a₂= b₁/b₂= c₁/c₂

From this we can decide the two lines are coincident. So  it is consistent. So there are infinitely many solution.

To obtain graph,we have make some changes in the first equation.

y = 5 - x


(ii) x - y = 8

   3 x - 3 y = 16

Solution:

      x -  y – 8 = 0

     3 x - 3 y -16 = 0

From the above information let us take the values of a₁, a₂, b₁, b₂, c₁ and c₂

 a₁ = 1          b₁ = -1            c₁ = -8

 a₂ = 3         b₂ = -3            c₂ = -16

a₁/a₂ = 1/3

b₁/b₂ = -1/-3 = 1/3

c₁/c₂ = -8/-16 = 1/2

This exactly matches the condition a₁/a₂ = b₁/b₂ ≠ c₁/c₂

From this we can decide the two lines are parallel. It means these two lines will not intersect each other.

So it is inconsistent.


(iii)  2 x + y - 6 = 0

       4 x - 2 y - 4 = 0

Solution:

From the above information let us take the values of a₁, a₂, b₁, b₂, c₁ and c₂

 a₁ = 2             b₁ = 1                c₁ = -6

 a₂ = 4             b₂= -2               c₂ = -4

a₁/a₂ = 2/4 = 1/2

b₁/b₂ = 1/-2 = - 1/2

c₁/c₂ = -6/-4 = 3/2

This exactly matches the condition a₁/a₂ ≠ b₁/b₂

From this we can decide the two lines are intersecting. So it is consistent.

To find that unique solution we have to draw the graph for that we have make some changes in the given equation.

y = 6 - 2 x ------- (1)

2 y = 4 x - 4

y = 2 (2 x - 2)/2

y = 2 x - 2  ------- (2)

Those two lines are intersecting at the point (2,2). Therefore the solution is x = 2 and y = 2.


(iv)  2 x - 2 y - 2  = 0

       4 x - 4 y  - 5 = 0

Solution:

From the above information let us take the values of a₁, a₂, b₁, b₂, c₁ and c₂

 a₁ = 2          b₁ = -2            c₁ = -2

 a₂ = 4          b₂ = -4            c₂ = -5

a₁/a₂ = 2/4 = 1/2

b₁/b₂ = -2/-4 = 1/2

c₁/c₂ = -2/-5 = 2/5

This exactly matches the condition a₁/a₂ = b₁/b₂ ≠ c₁/c₂

From this we can decide the two lines are parallel. It means these two lines will not intersect each other.

So it is inconsistent.




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