Find the real values of x and y for which:



Consider,



Taking LCM




Putting i2 = -1





⇒ 4x + 2xi – 3i – 3 + 9y – 7iy = 10i


⇒ (4x – 3 + 9y) + i(2x – 3 – 7y) = 10i


Comparing the real parts, we get


4x – 3 + 9y = 0


⇒ 4x + 9y = 3 …(i)


Comparing the imaginary parts, we get


2x – 3 – 7y = 10


⇒ 2x – 7y = 10 + 3


⇒ 2x – 7y = 13 …(ii)


Multiply the eq. (ii) by 2, we get


4x – 14y = 26 …(iii)


Subtracting eq. (i) from (iii), we get


4x – 14y – (4x + 9y) = 26 – 3


⇒ 4x – 14y – 4x – 9y = 23


⇒ -23y = 23


⇒ y = -1


Putting the value of y = -1 in eq. (i), we get


4x + 9(-1) = 3


⇒ 4x – 9 = 3


⇒ 4x = 12


⇒ x = 3


Hence, the value of x = 3 and y = -1


1
1