Solve for x and y:
We have
and
Lets simplify these equations. Assuming p = 1/(3x + 2y) and q = 1/(3x – 2y),
2p + 3q = 17/5
⇒ 10p + 15q = 17 …(i)
Also,
⇒ 5p + q = 2 …(ii)
To solve these equations, we need to make one of the variables (in both the equations) have same coefficient.
Multiply equation (ii) by 2, so that the variable p in both the equations have same coefficient.
Recalling equations (i) and (ii),
10p + 15q = 17
5p + q = 2 [×2
⇒ 13q = 13
⇒ q = 1
Substitute q = 1 in eq.(i)/eq.(ii), as per convenience of solving.
Thus, substituting in eq.(ii), we get
5p + 1 = 2
⇒ 5p = 1
⇒ p = 1/5
Thus, p = 1/5 and q = 1
As p = 1/(3x + 2y),
⇒
⇒ 3x + 2y = 5 …(iii)
And q = 1/(3x – 2y)
⇒
⇒ 3x – 2y = 1 …(iv)
Adding equations (iii) and (iv) to obtain x and y,
(3x + 2y) + (3x – 2y) = 5 + 1
⇒ 6x = 6
⇒ x = 1
Putting the value of x in equation (iv), we get
3(1) – 2y = 1
⇒ 3 – 2y = 1
⇒ 2y = 2
⇒ y = 1
Hence, we have x = 1 and y = 1