Question

How many solutions does the system have? 4x-2y=82x+y=2

Answer 1

As the given equations are:

`\begin{gathered} 4x-2y=8 \\ 2x+y=2 \end{gathered}`

By simplifying the first equation:

`2x-y=4`

Now add the 3rd and 2nd equation:

`\begin{gathered} (2x+y)+(2x-y)=2+4 \\ 4x=6 \\ x=(6)/(4) \\ x=(3)/(2) \end{gathered}`

Now put the value of x in 2nd equation:

`\begin{gathered} 2*(3)/(2)+y=2 \\ 3+y=2 \\ y=-1 \end{gathered}`

So there is only one solution (3/2, -1)