Q. 403.8( 19 Votes )
Solve for x and y:
x + y = a + b,
ax - by = a2 - b2.
x + y = a + b …(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, so that variable y in both the equations have same coefficient.
Recalling equations 1 & 2,
x + y = a + b [×b
ax – by = a2 – b2
⇒ bx + ax = ab + a2
⇒ (b + a)x = a(a + b)
⇒ x = a
Substitute x = a in equations (i)/(ii), as per convenience of solving.
Thus, substituting in equation (i), we get
a + y = a + b
⇒ y = b
Hence, we have x = a and y = b.
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