Question

Solve by cross- Multiplication method: x + y = a-b ; ax - by = a2 + b2. ​

Answer 1

Answer:

x=a,y=b

Step-by-step explanation:

The given system of equations may be written as

x+y−(a+b)=0

ax−by−(a  2  −b  2  )=0

By cross-multiplication, we get

−(a  2  −b  2  )−(−b)×−(a+b) x

​   =  −(a  2 −b  2  )−a×−(a+b) −y

​   =  1×−b−a×1 1

​  ⇒  −a  2 +b  2  −ab−b  2 x

​  =  −a  2 +b  2 +a  2  +ab −y

​  =  −b−a 1

​  ⇒  −a(a+b) x

​ =  b(a+b) −y

​   =  −(a+b) 1

​  ⇒  −a(a+b) x

​   =  −b(a+b) y

​   =  −(a+b) 1

​  ⇒x=  −(a+b) −a(a+b)

​  =a and y=  −(a+b) −b(a+b)

​   =b

Hence, the solution of the given system of equations is x=a,y=b

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