Question

Solve the following system of linear equation.

2(ax-by)+( a +4b) =0,2(bx-ay)+b(b-4a)=0

Answer 1

Answer:

The given equation may be written as

2ax-2by= -a-4b. .......(1)

2bx+2ay=4a-b. ...(2)

Multiplying eq.1 by and 2 by b and adding ,we get

(2a^2+2b^2)x=(-a^2b^2)

2(a^2+b^2)x=-(a^2+b^2)

or x=-1/2.

putting x=-1/2in eq.1 ,we get

2a {-1/2}-2by=-a-4b

Or-a-2by=-a-4b

Or 2by =4b

Or y=4b/2b=2

Hence ,x=-1/2 and y=2.

Answer 2

Answer:

The given equation may be written as

2ax-2by= -a-4b. .......(1)

2bx+2ay=4a-b. ...(2)

Multiplying eq.1 by and 2 by b and adding ,we get

(2a^2+2b^2)x=(-a^2b^2)

2(a^2+b^2)x=-(a^2+b^2)

or x=-1/2.

putting x=-1/2in eq.1 ,we get

2a {-1/2}-2by=-a-4b

Or-a-2by=-a-4b

Or 2by =4b

Or y=4b/2b=2

Hence ,x=-1/2 and y=2.