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in Linear Equations by (40 points)
\( 4 x+\frac{y}{3}=\frac{8}{3} ; \frac{x}{2}+\frac{y}{4}=\frac{-5}{2} \)

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1 Answer

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by (40.5k points)

\(4x +\frac{y}{3} =\frac {8}{3}\)

⇒ 12 x + y = 8  — (1) ( on multiplying both sides by 3)

and \(\frac{x}{2}+\frac{y}{4}=-\frac{5}{2}\)

⇒ 2x + y = -10 — (2) ( on multiplying both sides by 4)

subtract equation (2) from (1) , we get

(12x+y) - (2x+y) = 8 - (-10)

⇒ 10x = 18

⇒ x = \(\frac{18}{10}=\frac{9}{5} \)

∴ from (2), we obtain

\(\frac{18}{5}+y=-10\)

⇒ y = -10 - \(\frac{18}{5}\) = \(\frac{−50−18}{5}=\frac{−68}{5}\)

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