Question

(a+b)(x+y)=4ab (a-b)x +(a+b)y=2a^2-2b^2
Find x and y by cross multiplication method Plus fast

Answer 1

Answer:

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Step-by-step explanation:

The given system of equations are:

(a - b)x + (a + b)y = 2a2 - 2b2

So, (a - b)x + (a + b)y - 2a2 - 2b2 = 0

(a - b)x + (a + b)y - 2(a2 - b2) = 0 ........(i)

And (a + b)(x + y) = 4ab

So, (a +b)x + (a + b)y - 4ab = 0 ..........(ii)

The given system of equation is in the form of

a1x + b1y - c1 = 0

and a2x + b2y - c2 = 0

Compare (i) and (ii) , we get

a1 = a - b, b1 = a + b, c1 = -2(a2 + b2)

a2 = a + b, b2 = a + b, c2 = -4ab

By cross-multiplication method

x2(a+b)(a2−b2+2ab) =−y2(a−b)(a2+b2) =1−2b(a+b)

Now, x2(a+b)(a2−b2+2ab)=1−2b(a+b)  

⇒x=2ab−a2+b2b

And, −y2(a−b)(a2+b2)=1−2b(a+b)  

⇒y=(a−b)(a2−b2)b(a+b)

The solution of the system of equations are 2ab−a2+b2b and (a−b)(a2−b2)b(a+b)