Question

What is the solution of the system:y = 1/2x + 4-x+2y=8

Answer 1

Given the following system of equations:

`\begin{cases}y=(1)/(2)x+4 \\ -x+2y=8\end{cases}`

notice that we can use the first equation and substitute it on the second equation to get the following:

`-x+2((1)/(2)x+4)=8`

then, solving for 'x', we get:

`\begin{gathered} -x+2((1)/(2)x+4)=8 \\ \Rightarrow-x+x+8=8 \\ \Rightarrow8=8 \end{gathered}`

since the variable x was eliminated in the process of solving for it, we have that both equations represent the same line, therefore, there are infinite solutions for the system