Question

Solve the following pair of linear equation by substituting method
1
$2(ax - by) + (a + 4y) = 0 \\ 2(bx - ay) + (b - 4a) = 0$

Answer 1

2(ax-by)+a+4b=0                                                                        ..................1
2(bx+ay)+b-4a=0                                                                         ..................2
From Equation 1
   2(ax-by)+a+4b=0
=> 2ax -2by+a+4b =0
=> 2ax-2by= -(a+4b)                                                                    .....................3
From Equation 2
2(bx+ay)+b-4a=0
2bx + 2AY +b - 4a=0
2bx+2ay = -(b-4a)                                                                        ......................4
Solving equation 3 and 4 by elimation method
Multiplying equation 3 by a and 2 by b
New equation we get is
Adding the equations
2aax-2aby= -aa+4ab
2bbx+2aby= -bb-4ab

(2aa+2bb)x = -(aa+bb)
2(aa+bb)x = -(aa+bb)
2x= -1
x= -1/2                                      ...............5

 Putting the value of x in equation 4
2bx+2ay =-(a+4b)
-b+2ay=-a-4b
2ay = a-3b
y=a-3b/2a