Math, asked by faisalniazi6699, 22 days ago

Solve for x and y: 3/x + 4/y = 1 ; 4/x + 2/y = 11/12​

Answers

Answered by anindyaadhikari13
13

\texttt{\textsf{\large{\underline{Solution}:}}}

Given Equations:

 \rm \longmapsto  \dfrac{3}{x} +  \dfrac{4}{y} = 1  \: - (i)

 \rm \longmapsto  \dfrac{4}{x} +  \dfrac{2}{y} =  \dfrac{11}{12}   \: - (ii)

We have to find out the values of x and y.

Multiplying equation (ii) by 2, we get:

 \rm \longmapsto  \dfrac{8}{x} +  \dfrac{4}{y} =  \dfrac{11}{6}   \: - (iii)

Subtracting (i) from (iii), we get:

 \rm \longmapsto  \dfrac{5}{x} = \dfrac{11}{6} - 1

 \rm \longmapsto  \dfrac{5}{x} = \dfrac{11 - 6}{6}

 \rm \longmapsto  \dfrac{5}{x} = \dfrac{5}{6}

 \rm \longmapsto  \dfrac{1}{x} = \dfrac{1}{6}

 \rm \longmapsto x =6

Substituting the value of x in (i), we get:

 \rm \longmapsto  \dfrac{3}{6} +  \dfrac{4}{y} = 1

 \rm \longmapsto  \dfrac{1}{2} +  \dfrac{4}{y} = 1

 \rm \longmapsto \dfrac{4}{y} = 1  -  \dfrac{1}{2}

 \rm \longmapsto \dfrac{4}{y} = \dfrac{1}{2}

 \rm \longmapsto y = 4 \times 2

 \rm \longmapsto y = 8

Therefore:

 \rm \longmapsto \begin{cases} \rm x = 6 \\ \rm y = 8 \end{cases}  \: \:( Answer)

\texttt{\textsf{\large{\underline{Answer}:}}}

  • The values of x and y are 6 and 8.
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