Question

a x
$ax + by = b - a \: \: \: \: \: \: bx - ay \: = - (a + b)$
​

Answer 1

Answer:

x = –1 , y = 1

Solution:

Here,

The given equations are:

ax + by = b - a --------(1)

bx - ay = -(a+b) ------(2)

Now,

Multiplying eq-(1) with a , we get ;

=> a•( ax + by ) = a•( b - a )

=> a²x + aby = ab - a² -------(3)

Also,

Multiplying eq-(2) with b , we get ;

=> b•( bx - ay ) = b•[ -(a+b) ]

=> b²x - aby = -ab - b² -----(4)

Now,

Adding eq-(3) and (4) , we get ;

=> a²x + aby + b²x - aby = ab - a² - ab - b²

=> a²x + b²x = - a² - b²

=> x(a² + b²) = -(a² + b²)

=> x = -(a² + b²)/(a² + b²)

=> x = -1

Now,

Putting x = -1 in eq-(1) , we get ;

=> ax + by = b - a

=> a•(-1) + by = b - a

=> -a + by = b - a

=> by = b - a + a

=> by = b

=> y = b/b

=> y = 1

Hence,

The required answer is :

x = –1 , y = 1

Answer 2

Answer:

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