Question

ax+by-a+b=0
bx-ay-a-b=0
Solve x and y

Answer 1

Given :-

• $\rm\:ax+by-a+b=0$

• $\rm\:bx-ay-a-b=0$

To find :-

• Value of x and y = ?

Solution :-

The equations may be written as,

$\rm\:ax+by=a-b\:........................(i)$

$\rm\:bx-ay=a+b\:........................(ii)$

Multiplying eq (i) by a and eq (ii) by b,we get

$\rm\:{a}^{2}x+aby={a}^{2}-ab\:............(iii)$

$\rm\:{b}^{2}x-aby=ab+{b}^{2}\:............(iv)$

Adding eq (iii) and eq (iv), we get

$\rm\:({a}^{2}+{b}^{2})x=({a}^{2}+{b}^{2})$

$\rm\longrightarrow\:x=\dfrac{{(a}^{2}+{b}^{2})}{{(a}^{2}+{b}^{2})}$

$\rm\longrightarrow\:x=1$

Now,

Putting x = 1 in eq (i) we get,

$\rm\:(a\times\:1)+by=a-b$

$\rm\longrightarrow\:a+by=a-b$

$\rm\longrightarrow\:by=a-b-a$

$\rm\longrightarrow\:by=-b$

$\rm\longrightarrow\:y=\dfrac{-b}{b}$

$\rm\longrightarrow\:y=-1$

$\rm\therefore\:x=1\:\:\:\:y=-1$