Q. 463.8( 15 Votes )
Solve for x and y:
bx - ay + 2ab = 0.
⇒ b2x – a2y + a2b + ab2 = 0
⇒ a2y – b2x = a2b + ab2 …(i)
bx – ay = - 2ab
⇒ ay – bx = 2ab …(ii)
To solve these equations, we need to make one of the variables (in both the equations) have same coefficient.
Lets multiply equation (ii) by b, so that variable y in both the equations have same coefficient.
Recalling equations (i) & (ii),
a2y – b2x = a2b + ab2
ay – bx = 2ab [×b]
⇒ a2y – aby = a2b – ab2
⇒ (a2 – ab)y = a2b – ab2
⇒ a(a – b)y = ab(a – b)
⇒ y = b
Substitute y = b in equations (i)/(ii), as per convenience of solving.
Thus, substituting in equation (ii), we get
a(b) – bx = 2ab
⇒ ab – bx = 2ab
⇒ bx = ab – 2ab = - ab
⇒ x = - a
Hence, we have x = - a and y = b.
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