Question

To investigate the condition for consistency and inconsistency of three pair of linear equation graphically
(1) 2x+y=2;4x+2y=8
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Answer 1

Answer

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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:

[1] y = -2x + 4

// Plug this in for variable y in equation [2]

[2] 4x - 2•(-2x+4) = 8

[2] 8x = 16

// Solve equation [2] for the variable x

[2] 8x = 16

[2] x = 2

// By now we know this much :

x = 2

y = -2x+4

// Use the x value to solve for y

y = -2(2)+4 = 0

Solution :

{x,y} = {2,0}