​ Solve the following systems of equations: x/7 + y/3 = 5 x/2 - y/9 = 6 ​

Question

Solve the following systems of equations:

\(\frac{x}{7}\)+ \(\frac{y}{3}\) = 5

 \(\frac{x}{2}\)- \(\frac{y}{9}\) = 6

Answer 1

 \(\frac{x}{7}\)+ \(\frac{y}{3}\) = 5

⇒ 3x + 7y = 105

 \(\frac{x}{2}\)- \(\frac{y}{9}\) = 6

⇒ 9x – 2y = 108

Multiplying eq1 by 3 and subtracting eq2 from it

⇒ 9x + 21y – 9x + 2y = 315 – 108

⇒ 23y = 207

⇒ y = 9

Thus,

9x – 18 = 108

⇒ x = 14