(a-b)x+(a+b)y=a2-2ab-b2 (a+b)(x+y)=a2+b2 By Elimination Method

3 min read Jun 16, 2024

Solving the System of Equations by Elimination Method

We are given the following system of equations:

(1) (a - b)x + (a + b)y = a² - 2ab - b²

(2) (a + b)(x + y) = a² + b²

Our goal is to solve for x and y using the elimination method.

First, we need to simplify equation (2) to make it easier to work with:

(2) (a + b)x + (a + b)y = a² + b²

Now, let's arrange both equations so that the x and y terms are aligned:

(1) (a - b)x + (a + b)y = a² - 2ab - b²

(2) (a + b)x + (a + b)y = a² + b²

To eliminate y, we can multiply equation (2) by -1:

(1) (a - b)x + (a + b)y = a² - 2ab - b²

(2) -(a + b)x - (a + b)y = -a² - b²

Now, adding the two equations together, the y terms cancel out:

(1) + (2) (a - b)x - (a + b)x = a² - 2ab - b² - a² - b²

Simplifying, we get:

-2bx = -2ab - 2b²

Dividing both sides by -2b:

x = a + b

Now that we know the value of x, we can substitute it into either of the original equations to solve for y. Let's use equation (1):

(1) (a - b)(a + b) + (a + b)y = a² - 2ab - b²

Simplifying:

a² - b² + (a + b)y = a² - 2ab - b²

Canceling out the a² and b² terms:

(a + b)y = -2ab

Dividing both sides by (a + b):

y = -2a

Therefore, the solution to the system of equations is: