​ Solve the following systems of equations: 3x - (y+7)/11 + 2 = 10 2y - (x-11)/7 = 10 ​

Question

Solve the following systems of equations:

3x - \(\frac{y+7}{11}\) + 2 = 10

2y - \(\frac{x+11}{7}\) = 10

Answer 1

Consider,

3x - \(\frac{y+7}{11}\) + 2 = 10

⇒ 33x - y - 7 + 22 = 110

⇒ 33x - y - 95 = 0

⇒ 33x - 95 = y ...... (1)

Consider,

2y - \(\frac{x+11}{7}\) = 10

⇒ 14y + x + 11 = 70

⇒ 14y + x = 59 .... (2)

Put the value of y from (1) in (2) to get,

4(33x-95) + x

= 59 462x - 1330 + x

= 59463x

= 1389x

= 3

Put the value of x in (1) to get,

33(3) - 95 = y

99 - 95 = y

4 = y

⇒ x = 3 and y = 4