Question

solve for x and y

bx - ay= a²b - ab²
ax + by = a³ + b³​

Answer 1

Answer:

The value of x and y are a² and b² respectively.

Given:

The given equations are

bx - ay = a²b - ab² and ax + by = a³ + b³.

To find:

• The values of x and y.

Solution:

=> bx - ay = a²b - ab²...(1)

=> ax + by = a³ + b³...(2)

Multiply equation (1) by b we get,

=> b²x - aby = a²b² - ab³...(3)

Multiply equation (2) by a we get,

=> a²x + aby = a⁴ + ab³...(4)

Add equations (3) and (4), we get

⠀b²x - aby = a²b² - ab³

+

⠀a²x + aby = a⁴ + ab³

____________________

⠀⠀⠀=> a²x + b²x = a⁴ + a²b²

⠀⠀⠀=> x (a² + b²) = a² (a² + b²)

⠀⠀⠀=> x = a²

Substitute x = a² in equation (2), we get

⠀⠀⠀=> a (a²) + by = a³ + b³

⠀⠀⠀=> a³ + by = a³ + b³

⠀⠀⠀=> by = b³

⠀⠀⠀=> y = b³/b

⠀⠀⠀=> y = b²

Therefore, the value of x and y are a² and b² respectively.