Solve for x and y:
a2x + b2y = c2, b2x + a2y = d2
a2x + b2y = c2 …(i)
b2x + a2y = d2…(ii)
To solve these equations, we need to simplify them.
So, by adding equations (i) and (ii), we get
(a2x + b2y) + (b2x + a2y) = c2 + d2
⇒ (a2x + b2x) + (b2y + a2y) = c2 + d2
⇒ (a2 + b2)x + (a2 + b2)y = c2 + d2
Now dividing it by (a2 + b2), we get
x + y = (c2 + d2)/( a2 + b2) …(iii)
Similarly, subtracting equations (i) and (ii),
(a2x + b2y) – (b2x + a2y) = c2 – d2
⇒ (a2x – b2x) – (b2y – a2y) = c2 – d2
⇒ (a2 – b2)x – (a2 – b2)y = c2 – d2
Dividing the equation by (a2 – b2), we get
x – y = (c2 – d2)/ (a2 – b2) …(iv)
To solve equations (iii) and (iv), we need to make one of the variables (in both the equations) have same coefficient.
Here the variables x in both the equations have same coefficients.
Substitute in eq.(iii)/eq.(iv), as per convenience of solving.
Thus, substituting in eq.(iii), we get
Hence, we have and .
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