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:

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

Now put the value of x in 2nd equation:

$\begin{gathered} 2\times\frac{3}{2}+y=2 \\ 3+y=2 \\ y=-1 \end{gathered}$

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