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

**(i) **

Comparing equation with

and with , we get

and

and

We have which means that equations have infinite many solutions because they are coincident.

**Hence they are consistent.**

To represent equations graphically, we will plot both of the lines.

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

**(Blue)** and **(Red)**

We can see that both of the lines coincide. Hence, there are infinite many solutions. Any point which lies on one line also lies on the other. Hence, by using equation , we can say that

We can assume any random values for y and can find the corresponding value of x using the above equation. All such points will lie on both lines and there will be infinite number of such points.

**(ii) **

Comparing equation with

and with , we get

and

and

We have

Lines are parallel to each other which means they have no solution.

**Therefore, equations are inconsistent. **

**(iii) **

Comparing equation with

and with , we get

and

and

We have

, which means that they have unique solution.

**Hence, they are consistent.**

To obtain solution graphically, we will plot both of the lines.

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

**(Blue)** and **(Red)**

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

**(iv) **

Comparing equation with

and with , we get

and

and

Therefore, we have

The lines are parallel which means that they have no solution.

**Hence, the equations are inconsistent.**