Question

Use elimination to solve the system of equations. - 3x – 2y = -5 7x + y = 1

Answer 1

Given the following system of equations:

`\begin{cases}-3x-2y=-5 \\ 7x+y=1\end{cases}`

notice that we can multiply by 2 the second equation to get:

`2\cdot(7x+y=1)=14x+2y=2`

then, we can add both equations to get the following:

`\begin{gathered} 14x+2y=2 \\ -3x-2y=-5 \\ ---------- \\ 11x=-3 \\ \Rightarrow x=-(3)/(11) \end{gathered}`

Now that we have that x=-3/11, we can use this value to find y on the original second equation:

`\begin{gathered} 7(-(3)/(11))+y=1 \\ \Rightarrow-(21)/(11)+y=1 \\ \Rightarrow y=1+(21)/(11)=(11)/(11)+(21)/(11)=(32)/(11) \\ y=(32)/(11) \end{gathered}`

therefore, the solution of the syste is (-3/11,32/11)