NCERT solution Class 10 pair of linear equations in two variables

NCERT Solutions

Class 10 Maths

Pair of Linear Equations in Two Variables

NCERT Questions

Ex. 3.1 Q.1
Ex.3.1 Q.2
Ex.3.1 Q.3
Ex.3.1 Q.4
Ex.3.1 Q.5
Ex.3.1 Q.6
Ex.3.1 Q.7
Ex.3.2 Q.1
Ex.3.2 Q.2
Ex.3.2 Q.3
Ex.3.3 Q.1
Ex.3.3 Q.2

Ex.3.1 Q.4

Which of the following pairs of linear equations are consistent or inconsistent?

If consistent, obtain the solution graphically:

(1) x + y = 5, 2x + 2y = 10

(2) x – y = 8, 3x – 3y = 16

(3) 2x + y – 6 = 0, 4x – 2y – 4 = 0

(4) 2x – 2y – 2 = 0, 4x – 4y – 5 = 0

(1) x + y = 5; 2x + 2y = 10

= and

= =

Hence, = =

Therefore, these linear equations are coincident and have infinite number of possible solutions.

Therefore, the pair of linear equations is consistent.

x + y = 5

x = 5 – y

X	4	3	2
Y	1	2	3

and,

2x + 2y = 10

x = (10 – 2y) ÷ 2

X	4	3	2
Y	1	2	3

Graphical representation

From the figure, it can be observed that these lines are overlapping each other.

Therefore, infinite number of solutions are possible for the given pair of equations.

(2) x – y = 8, 3x – 3y = 16

= = and

= =

Hence, = ≠

Therefore, these linear equations are parallel to each other and thus have no possible solution.

Hence, the pair of linear equations is inconsistent.

(3) 2x + y – 6 = 0, 4x – 2y – 4 = 0

= =

= – and

= =

Hence, ≠

Therefore, these linear equations are intersecting each other at one point

and thus have only one possible solution.

Hence, the pair of linear equations is consistent.

2x + y – 6 = 0

y = 6 – 2x

X	0	1	2
Y	6	4	2

and,

4x – 2y – 4 = 0

y = (4x – 4) ÷ 2

X	1	2	3
Y	0	2	4

Graphical representation is given below:

From the figure, it can be observed that these lines are intersecting each other at the only one point i.e., (2,2)

which is the solution for the given pair of equations.

(4) 2x – 2y – 2 = 0, 4x – 4y – 5 = 0

= =

= = and

Hence, = ≠ 2

Therefore, these linear equations are parallel to each other and thus, have no possible solution.

Hence, the pair of linear equations is inconsistent.

Video solution:

Pair of Linear Equations in Two Variables Class 10 Maths NCERT Chapter 3 NCERT Solutions

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