Solve the following systems of equations:\(\frac{1}{2x}\)+\(\frac{1}{3

1.	Solve the following systems of equations:\(\frac{1}{2x}\)+\(\frac{1}{3y}\) = 2\(\frac{1}{3x}\)+\(\frac{1}{2y}\) = \(\frac{13}{6}\)
Answer» \(\frac{1}{2x}\)+\(\frac{1}{3y}\) = 2 \(\frac{1}{3x}\)+\(\frac{1}{2y}\) = \(\frac{13}{6}\) Multiplying eq 1 by 1/2 and eq2 by 1/3 and subtracting ⇒ 1/4x – 1/9x = 1 – 13/18 ⇒ 5/36x = 5/18 ⇒ x = 1/2 Thus, 1 + 1/3y = 2 ⇒ y = 1/3

Solve the following systems of equations:\(\frac{1}{2x}\)+\(\frac{1}{3y}\) = 2\(\frac{1}{3x}\)+\(\frac{1}{2y}\) = \(\frac{13}{6}\)

Answer»

\(\frac{1}{2x}\)+\(\frac{1}{3y}\) = 2

\(\frac{1}{3x}\)+\(\frac{1}{2y}\) = \(\frac{13}{6}\)

Multiplying eq 1 by 1/2 and eq2 by 1/3 and subtracting

⇒ 1/4x – 1/9x = 1 – 13/18

⇒ 5/36x = 5/18

⇒ x = 1/2

Thus,

1 + 1/3y = 2

⇒ y = 1/3