Question

solve the following pair of linear equation for two variable for x and y . 2(ax-by)+(a+4b)=0 and 2(bx+ay)+(b-4a)​

Answer 1

Answer:

Solution : 

The given equations may be written as

2ax−2by=−a−4b 2ax-2by=-a-4b… (i)

2bx+2ay=4a−b 2bx+2ay=4a-b… (ii)

Multiplying (i) by a and (ii) by b and adding , we get

(2a2+2b2)x=(−a2−b2)(2a2+2b2)x=(-a2-b2)

⇒2(a2+b(2))x=−(a2+b2)⇒x=−12⇒2(a2+b(2))x=-(a2+b2)⇒x=-12

Putting x=−12x=-12 in (i), we get

2a×(−12)−2by=−a−4b2a×(-12)-2by=-a-4b

⇒−a−2by=−a−4b⇒-a-2by=-a-4b

⇒2by=4b⇒y=4b2b=2⇒2by=4b⇒y=4b2b=2

Hence, x=−12andy=2

Answer 2

Answer:

The given equations may be written as

2ax−2by=−a−4b 2ax-2by=-a-4b… (i)

2bx+2ay=4a−b 2bx+2ay=4a-b… (ii)

Multiplying (i) by a and (ii) by b and adding , we get

(2a2+2b2)x=(−a2−b2)(2a2+2b2)x=(-a2-b2)

⇒2(a2+b(2))x=−(a2+b2)⇒x=−12⇒2(a2+b(2))x=-(a2+b2)⇒x=-12

Putting x=−12x=-12 in (i), we get

2a×(−12)−2by=−a−4b2a×(-12)-2by=-a-4b

⇒−a−2by=−a−4b⇒-a-2by=-a-4b

⇒2by=4b⇒y=4b2b=2⇒2by=4b⇒y=4b2b=2

Hence, x=−12andy=2

Step-by-step explanation: