Question

Find the value of x and y in x+y=a+b and ax+by=a²-b²

Answer 1

Answer :

x = (a + b)(a - 2b) / (a - b)

y = b(a + b) / (a - b)

Solution :

★ Given equations :

• x + y = a + b ----------------(1)

• ax + by = a² - b² --------------(2)

★ To find :

• x = ?

• y = ?

Now ,

Multiplying eq-(1) by b , we have ;

=> b(x + y) = b(a + b)

=> bx + by = ab + b² -----------(3)

Now ,

Subtracting eq-(3) from (2) , we get ;

=> (ax + by) - (bx + by) = (a² - b²) - (ab + b²)

=> ax + by - bx - by = (a+b)(a-b) - b(a+b)

=> ax - bx = (a + b)(a - b - b)

=> x(a - b) = (a + b)(a - 2b)

=> x = (a + b)(a - 2b) / (a - b)

Now ,

Putting x = (a + b)(a - 2b) / (a - b) in eq-(1) ,

We get ;

=> x + y = a + b

=> y = (a + b) - x

=> y = (a + b) - (a + b)(a - 2b) / (a - b)

=> y = (a + b)•[ 1 - (a - 2b) / (a - b) ]

=> y = (a + b)•[ (a - b) - (a - 2b) ] / (a - b)

=> y = (a + b)•[ a - b - a + 2b ] / (a - b)

=> y = (a + b)•b / (a - b)

=> y = b(a + b) / (a - b)

Hence ,

x = (a + b)(a - 2b) / (a - b)

y = b(a + b) / (a - b)