Question

2(ax-by) +a+4b=0
2(bx+ay) +b-4a=0
Solve it by elimination or substitution method

Answer 1

Step-by-step explanation:

You can write these equations like :

2ax - 2by = -a-4b   ..... (1)

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

Now, multiplying (1) by a & (2) by b,

2a^2x - 2aby = -a^2 - 4ab ......(3)

2b^2x + 2aby = -b^2 + 4ab .....(4)

Adding (3) & (4),

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

Obviously, x = -1/2.

Answer 2

Answer:

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

2ax - 2by = -a - 4b - - - - - - - - (1) a²

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

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

Multiplying the equation (1) by a & Equation (2) by b we get

2a²x - 2aby = - a² - 4ab - - - - - - - (3)

2b²x + 2aby = 4ab - b² - - - - - - - (4)

On addition

2a²x + 2b²x = - ( a² + b²)

2( a² + b²) x = - ( a² + b²)

x = - 1/2

From Equation (1)

-a - 2by = - a - 4b

-2by = - 4b

y = 2

Hence the required solution is

x = - 1/2, y = 2

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