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 

Here, $\frac{a_1}{a_2}=\frac{1}{2}$, $\frac{b_1}{b_2}=\frac{1}{2}$and $\frac{c_1}{c_2}=\frac{-10}{-5}=\frac{1}{2}$

Since, $\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$

∴ The equations are coincident and have infinite number of possible solutions. Hence, the equations are consistent.

For  x + y = 5, the solution table is:

For 2x + 2y = 10 , the solution table is:

Graphical representation is shown below:

Since the lines are overlapping each other, therefore, the equations have infinite possible solutions.