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