question_answer

Solve by elimination:

\[3x=y+5\]

\[5x-y=11\]

Answer:

Given equations are,

\[3x=y+5\]                                                 ...(i)

\[5x-y=11\]                                                  ...(ii)

On subtracting eq. (i) and (ii), we get

\[_{\begin{smallmatrix}  5x\,\,-\,\,y\,\,=\,\,11 \\  -\,\,\,\,\,\,+\,\,\,\,\,\,\,-  \\  \overline{-2x\,\,\,\,\,\,\,\,=\,\,-6} \end{smallmatrix}}^{3x\,\,-\,\,y\,\,=\,\,5}\]

\[x=3\]

Putting the value of x in eq. (i)

\[3(3)-y=5\]

\[9-5=y\]

\[\Rightarrow y=4\]

\[\therefore x=3,y=4\]