Q. 454.4( 7 Votes )
Solve for x and y:
ax - by = a2 + b2, x + y = 2a
ax – by = a2 + b2 …(i)
x + y = 2a …(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),
ax – by = a2 + b2
x + y = 2a [×b
⇒ ax + bx = a2 + b2 + 2ab
⇒ (a + b)x = (a + b)2
⇒ x = a + b
Substitute x = (a + b) in equations (i)/(ii), as per convenience of solving.
Thus, substituting in equation (ii), we get
a + b + y = 2a
⇒ y = 2a – a – b
⇒ y = a – b
Hence, we have x = (a + b) and y = (a – b).
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