Question

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

Answer 1

The answer is below

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