Question

I need help seeing how this works out because what I am doing is not right

Answer 1

We will have the following:

AB and CD related in terms of x and y will be:

$\begin{gathered} AB=CD\Rightarrow x+y=2x-y-2 \\ \\ \Rightarrow2y=x-2\Rightarrow y=\frac{x}{2}-1 \end{gathered}$

So, the equation that relates AB and CD is:

$y=\frac{x}{2}-1$

BC and DA in terms of x and y is:

$\begin{gathered} BC=DA\Rightarrow x+2y=3x-3y+2 \\ \\ \Rightarrow5y=2x+2\Rightarrow y=\frac{2}{5}x+\frac{2}{5} \end{gathered}$

So, the equation that relates BC and DA is:

$y=\frac{2}{5}x+\frac{2}{5}$

Now; we determine the values of x & y as follows:

$\begin{gathered} \frac{x}{2}-1=\frac{2}{5}x+\frac{2}{5}\Rightarrow\frac{1}{10}x=\frac{7}{5} \\ \\ \Rightarrow x=14 \end{gathered}$

Then:

$y=\frac{(14)}{2}-1\Rightarrow y=6$

So, the values are:

$\begin{gathered} x=14 \\ \\ y=6 \end{gathered}$