### Chapter 3: Pair of Linear Equations in Two Variables

Q
##### Pair of linear equations in two variables CBSE NCERT Solutions

Question:

Which of the following pairs of linear equations are consistent/inconsistent? If consistent, obtain the solution graphically:

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

(ii) x - y = 8 , 3x - 3y = 16

(iii) 2x + y - 6 = 0 , 4x - 2y - 4 = 0

(iv) 2x - 2y - 2 = 0 , 4x - 4y - 5 = 0

(i)  x + y = 5 , 2x + 2y = 10

For equation x + y = 5,  we have the following points which lie on the line.

 x 0 5 y 5 0

For equation 2x + 2y – 10 = 0, we have the following points which lie on the line.

 x 1 2 y 4 3

We plot the points for both of the equations to find the solution.

We can see that both of the lines coincide. Hence, there are infinitely many solutions and lines are consistent.

(ii) x - y = 8 , 3x - 3y = 16

For x – y = 8, the coordinates are:

 x 0 8 y -8 0

And for 3x – 3y = 16, the coordinates are:

 x 0 $\frac{16}{3}$ y $-\frac{16}{3}$ 0

We plot the points for both of the equations to find the solution.

Plotting these points on the graph, it is clear that both lines are parallel. So the two lines have no common point. Hence the given equations have no solution and lines are inconsistent.

(iii) 2x + y - 6 = 0 , 4x - 2y - 4 = 0

For equation 2x + y – 6 = 0, we have the following points which lie on the line.

 x 0 3 y 6 0

For equation 4x – 2y – 4 = 0, we have the following points which lie on the line.

 x 0 1 y -2 0

We plot the points for both of the equations to find the solution.

We can see that lines are intersecting at (2, 2) which is the solution.

Hence x = 2 and y = 2 and lines are consistent.

(iv) 2x - 2y - 2 = 0 , 4x - 4y - 5 = 0

For 2x – 2y – 2 = 0, the coordinates are:

 x 2 0 y 0 -2

And for 4x – 4y – 5 = 0, the coordinates are:

 x 0 $\frac{5}{4}$ y $-\frac{5}{4}$ 0

We plot the points for both of the equations to find the solution.

Plotting these points on the graph, it is clear that both lines are parallel. So the two lines have no common point. Hence the given equations have no solution and lines are inconsistent.

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