Solve the following system of equations:x/7 + y/3 = 5;x/2 – y/9 = 6

1.	Solve the following system of equations:x/7 + y/3 = 5;x/2 – y/9 = 6
Answer» The given pair of equations are: x/7 + y/3 = 5……..(i) x/2 – y/9 = 6…….(ii) From (i), we get x/7 + y/3 = 5 ⇒ 3x + 7y = (5 x 21) [After taking LCM] ⇒ 3x = 105 – 7y ⇒ x = \(\frac{(105 – 7y)}{3}\)……. (iv) From (ii), we get x/2 – y/9 = 6 ⇒ 9x – 2y = 108 …………(iii) [After taking LCM] Now, substituting x in equation (iii) we get, 9[\(\frac{(105 − 7y)}{3}\)] – 2y = 108 ⇒ 945 – 63y – 6y = 324 [After taking LCM] ⇒ 945 – 324 = 69y ⇒ 69y = 621 ⇒ y = 9 Now, putting the value of y in the equation (iv) x = \(\frac{(105 − 7(9))}{3}\) ⇒ x = \(\frac{(105 − 63)}{3}\) = \(\frac{42}{3}\) ∴ x = 14 Thus, the value of x and y obtained are 14 and 9 respectively.

Answer»

The given pair of equations are:

x/7 + y/3 = 5……..(i)

x/2 – y/9 = 6…….(ii)

From (i), we get

x/7 + y/3 = 5

⇒ 3x + 7y = (5 x 21) [After taking LCM]

⇒ 3x = 105 – 7y

⇒ x = \(\frac{(105 – 7y)}{3}\)……. (iv)

From (ii), we get

x/2 – y/9 = 6

⇒ 9x – 2y = 108 …………(iii) [After taking LCM]

Now, substituting x in equation (iii) we get,

9[\(\frac{(105 − 7y)}{3}\)] – 2y = 108

⇒ 945 – 63y – 6y = 324 [After taking LCM]

⇒ 945 – 324 = 69y

⇒ 69y = 621

⇒ y = 9

Now, putting the value of y in the equation (iv)

x = \(\frac{(105 − 7(9))}{3}\)

⇒ x = \(\frac{(105 − 63)}{3}\) = \(\frac{42}{3}\)

∴ x = 14

Thus, the value of x and y obtained are 14 and 9 respectively.

Discussion