A x minus b y equal to a square + b square and X + y equal to 2
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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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