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​​

Answer 1

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(i) x+y=5   ...(i)

2x+2y=10    ...(ii)

⇒x+y=5

⇒y=5−x

 x 0 3 y 5 2Plot (0,5) and (3,5) on graph and join them to get equation x+y=5.

2x+2y=10

⇒2y=(10−2x)

⇒y=210−2x=5−x   ...(iii)

 x 5 2 y 0 3

So, the equation is consistent and has infinitely many solution

 

(ii) x−y=8   ....(i)

3x−3y=16   ....(ii)

⇒x−y=8

⇒−x+y=−8

⇒y=−8+x

⇒y=x−8

 x 8 0 y 0 -83x−3y=16   ...(ii)

⇒3x=16+3y

⇒3x−16=3y

⇒y=33x−16⇒y=x−316

 x 316 0 

Answer 2

Step-by-step explanation:

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