question_answer

Solve by elimination:

\[3x-y=7\]

\[2x+5y+1=0\]

Answer:

\[3x-y=7\]                                                         ...(i)

\[2x+5y=-1\]                                                                 ...(ii)

Multiplying equation (i) by 5 and solving it with equation (ii), we get

\[_{\begin{smallmatrix}  15x\,-\,5y\,=\,35 \\  \overline{17x\,\,\,\,\,\,\,\,\,\,\,\,\,=\,34\,\,} \end{smallmatrix}}^{2x\,\,+\,\,5y\,\,=\,\,-1}\]

(Adding)

\[\Rightarrow x=\frac{34}{17}=2\]

Putting the value of x in (i), we have

\[3(2)-y=7\]

\[\Rightarrow 6-y=7\Rightarrow -y=7-6\]

\[\Rightarrow y=-1\]

\[\therefore \,\,x=2,y=-1\]