Question

ax+by-a+b=0, bx-ay-a-b=0 find the valu of x and y​

Answer 1

Answer:

ax+by-a+b=0

ax+by=a-b_____(i)

bx-ay-a-b=0

bx-ay=a+b______(ii)

multiplying b with (i) and a with (ii), we get

abx + b^2 y = ab - b^2

-(abx - a^2 y = a^2 + ab)

-----------------------------------

(a^2 + b^2)y=(a^2-b^2)

multiplying by - both side

-(a^2 + b^2)y = - (a^2-b^2)

-(b^2 - a^2) y = -{(a+b)(a-b)}

(b-a)(b+a) y = -{(a+b)(a-b)}

y= -(a+b)(a-b)

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-(b+a)(b-a)

y= -(a-b)/-(b-a)

y= -(b-a)/b-a

y= -1

Putting the value of y in eq (i)

ax+by=a-b

ax+b(-1) =a - b

ax - b = a - b

ax = a

x = 1

Therefore the value of x=1 and y = -1