Q. 434.3( 15 Votes )
Solve for x and y:
ax + by = (a2 + b2)
⇒ bx – ay = 0 …(i)
ax + by = a2 + b2…(ii)
To solve these equations, we need to make one of the variables (in both the equations) have same coefficient.
Lets multiply equation (i) by b and (ii) by a, so that variable y in both the equations have same coefficient.
Recalling equations 1 & 2,
bx – ay = 0 [×b
ax + by = a2 + b2 [×a
b2x + a2x = a3 + ab2
⇒ (b2 + a2)x = a (a2 + b2)
⇒ (b2 + a2)x = a(b2 + a2)
⇒ x = a
Substitute x = a in equations (i)/(ii), as per convenience of solving.
Thus, substituting in equation (i), we get
ab – ay = 0
⇒ ay = ab
⇒ y = b
Hence, we have x = a and y = b.
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