Question

Solve the following system of linear equation by cross multiplication method.

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

Answer 1

Answer:

x = -1/2 , y = 2

Step-by-step explanation:

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

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

The equations become:

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

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

by Cross multiplication method,

        x                    y                  1

-2b            a+4b           2a                -2b

2a             b - 4a          2b                 2a

=> x/-2b(b-4a) - 2a(a+4b) = y/2b(a'+4b) -2a(b-4a)  = 1 / 4a² + 4b²

=> x/-2(b² + a²) = y/8(b² + a²) = 1/4(a² + b²)

=> x = -2(b² + a²) /4(a² + b²) = -1/2

=> y = 8(b² + a²)/4(a² + b²) = 2.