Question

Solve for x and y:
ax+by=a²
bx+ay=2ab

Answer 1

Answer:

Step-by-step explanation:

abx + a²y = 2 a²b/a²+b²

abx + b²y = 1

(-) (-) (-)

____________________

y(a²-b²) = (2a²b /a²+b²)-1

now solve it and find the value of y

->then put that value in any eq. and find the value of x

Answer 2

Given :

ax + by = a²

bx + ay  = 2ab

To Find : solve for x and y

Solution:

ax + by = a²

bx + ay  = 2ab

Adding both

(a + b)x  + (a + b) y = (a² + 2ab)

=> x + y  = (a² + 2ab)/(a + b)

ax + by = a²

bx + ay  = 2ab

on subtraction

x(a - b)  - y(a - b)  = (a² - 2ab)

=> x - y  =  (a² - 2ab)/ (a - b)

x + y  = a(a + 2b)/(a + b)

x - y  = a (a - 2b)/ (a - b)

Adding both

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

=> x = (a/2) (   (a + 2b) (a - b) + (a - 2b)(a + b) ) /(a² - b²)

=> x = (a/2) ( a² + 2ab - ab - 2b² + a² - 2ab + ab - 2b²) /(a² - b²)

=> x = (a/2)( 2a² - 4b²)/ (a² - b²)

=> x = a( a² - 2b²)/(a² - b²)

On subtraction

y = (a/2) (   (a + 2b) (a - b) - (a - 2b)(a + b) ) /(a² - b²)

=> y =  a²b/ (a² - b²)

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