Question

solve the following system of equations by elimination method x+y=a-b
ax-by=a²+b² ​
​

Answer 1

ax - by = a2 + b2
ax + ay = a2 - ab
—————————
-by -ay = b2 + ab
-y ( b + a ) = b ( b + a)
-y = b

y = -b

Putting in eq 1
x -b = a -b


x = a

Answer 2

Answer:

The given system of equations may be written as

x+y−(a+b)=0

ax−by−(a2−b2 )=0

By cross-multiplication, we get

________x_______

−(a2 −b2 )−(−b)×−(a+b) =

________y______

−(a2 −b2 )−a×−(a+b)− =

⇒

_____x____

−a2 +b2 −ab−b2 =

______-y______-__1__

−a2 +b2 +a2 +ab = −b−a

⇒

__x___-__-y__

−a(a+b) = b(a+b)

⇒

____x_________-_______-y____-__1__

−a2 +b2 −ab−b2 = −a2 +b2 +a2 +a= −b−a

1

⇒

__x__-__-y_____-__1__

−a(a+b = b(a+b) = −(a+b)

⇒

__x__

−a(a+b)

=

__y____-__1__

−b(a+b) = −(a+b)

⇒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.

=

__1__

−(a+b)

⇒

__x____-__y____-__1__

−a(a+b) = −b(a+b) = −(a+b)

⇒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.

Step-by-step explanation:

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

have a nice day...