question_answer

The solution of the pair of equation \[\frac{x}{2}+y=0.8\]and \[\frac{7}{x+\frac{y}{2}}=10\]is

A)  \[x=\frac{2}{5},\]\[y=\frac{3}{5}\]

B)  \[x=\frac{2}{3},\]\[y=5\]

C)  \[x=\frac{2}{5},\]\[y=\frac{5}{3}\]

D)  \[x=\frac{3}{5},\]\[y=\frac{2}{5}\]

Correct Answer: A

Solution :

Here, \[x+2y=1.6\]and \[x+\frac{y}{2}=\frac{z}{10}\]        (Given) \[\Rightarrow \]               \[10x+20y=16\] and                   \[10x+5y=7\]  On subtracting, we get \[\Rightarrow \]\[y=\frac{3}{5}\] From Eq. (i) \[x+2y=\frac{8}{5}\] Put       \[y=\frac{3}{5},\]\[x+\frac{6}{5}=\frac{8}{5}\] \[\Rightarrow \]               \[x=\frac{2}{5}\]