x-(a-c)y%3D2ab-(a%2Bb)x-(a-b)y%3D2ab.jpeg "(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.