Solve 2(ax-by)+(a+4b)=0, 2(bx+ay)+(b-4b) using linear equation

The answer is below

Step-by-step explanation:

2(ax-by)+(a+4b)=0                   .              .               .         1)

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

Equation 1 gives:

2ax - 2by + a + 4b = 0          .                .             .      1)

Equation 2 gives:

2bx + 2ay + b - 4a    =    0     .              .                   .     1)

Multiplying equation 1 by a and equation 2 by b :

2a²x - 2aby + a² + 4ab = 0

2b²x + 2aby + b² - 4ab = 0

Adding together:

2a²x  +  2b²x + a² + b² = 0

2x (a² + b²) = -(a² + b²)

2x = -1

x = -1/2

Multiplying equation 1 by b and equation 2 by a:

2abx · 2b²y + ab + 4b² = 0

2abx + 2a²y + ab - 4a² = 0

Subtracting:

2y(a² + b²) - 4(a² + b²) = 0

2y(a² + b²) = 4(a² + b²)

2y = 4

y = 2