(a+c)x-(a-c)y=2ab (a+b)x-(a-b)y=2ab

3 min read Jun 16, 2024
(a+c)x-(a-c)y=2ab (a+b)x-(a-b)y=2ab

Solving the System of Equations: (a+c)x-(a-c)y=2ab and (a+b)x-(a-b)y=2ab

This article will guide you through the process of solving the system of equations:

(a+c)x-(a-c)y=2ab

(a+b)x-(a-b)y=2ab

We will utilize the elimination method to solve for the variables 'x' and 'y'.

Step 1: Identify the Coefficients

Notice that the coefficients of 'y' in both equations are the same, but with opposite signs. This sets the stage for easy elimination.

Step 2: Eliminate 'y'

Subtract the second equation from the first equation:

(a+c)x-(a-c)y - [(a+b)x-(a-b)y] = 2ab - 2ab

Simplifying the equation:

(a+c)x - (a-c)y - (a+b)x + (a-b)y = 0

(a+c)x - (a+b)x - (a-c)y + (a-b)y = 0

(c-b)x = 0

Step 3: Solve for 'x'

Since the coefficient of 'y' has been eliminated, we can solve for 'x':

x = 0 / (c-b)

x = 0

Therefore, the value of 'x' is 0.

Step 4: Substitute 'x' to Find 'y'

Substitute the value of 'x' (0) into either of the original equations. Let's use the first equation:

(a+c)(0) - (a-c)y = 2ab

Simplifying the equation:

-(a-c)y = 2ab

y = -2ab / (a-c)

Therefore, the value of 'y' is -2ab / (a-c).

Conclusion

The solution to the system of equations is:

x = 0

y = -2ab / (a-c)

It's important to note that this solution is valid as long as (a-c) ≠ 0. If (a-c) = 0, then the system of equations would have no unique solution, as the two equations would represent the same line.

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