Given the following system of equations:
[tex]\begin{cases}-3x-2y=-5 \\ 7x+y=1\end{cases}[/tex]notice that we can multiply by 2 the second equation to get:
[tex]2\cdot(7x+y=1)=14x+2y=2[/tex]then, we can add both equations to get the following:
[tex]\begin{gathered} 14x+2y=2 \\ -3x-2y=-5 \\ ---------- \\ 11x=-3 \\ \Rightarrow x=-\frac{3}{11} \end{gathered}[/tex]Now that we have that x=-3/11, we can use this value to find y on the original second equation:
[tex]\begin{gathered} 7(-\frac{3}{11})+y=1 \\ \Rightarrow-\frac{21}{11}+y=1 \\ \Rightarrow y=1+\frac{21}{11}=\frac{11}{11}+\frac{21}{11}=\frac{32}{11} \\ y=\frac{32}{11} \end{gathered}[/tex]therefore, the solution of the syste is (-3/11,32/11)
