Question

What is the solution of {x+y=-1 {x-y=11

Answer 1

Use the elimination method to solve the given system of equations:

`\begin{gathered} x+y=-1 \\ x-y=11 \end{gathered}`

To do so, add both equations: right hand side plus right hand side equals left hand side plus left hand side:

`\begin{gathered} \Rightarrow(x+y)+(x-y)=(-1)+(11) \\ \Rightarrow x+y+x-y=-1+11 \\ \Rightarrow2x=10 \\ \Rightarrow x=(10)/(2) \\ \Rightarrow x=5 \end{gathered}`

Substitute x=5 into the first equation and solve for y:

`\begin{gathered} x+y=-1 \\ \Rightarrow5+y=-1 \\ \Rightarrow y=-1-5 \\ \Rightarrow y=-6 \end{gathered}`

Therefore, the solution for this system, is:

`\begin{gathered} x=5 \\ y=-6 \end{gathered}`