+40 Find the ordered pair \((x,y)\) if:
\( \begin{align*} x+y&=(5-x)+(5-y),\\ x-y&=(x-1)+(y-1). \end{align*}\)
+1926 Let's first take a look at the first equation. We want to put x in terms of y.
So, solving the equation, we have
\(x+y=10-x-y\\ x=5-y\)
Now, subsituting this into the second equation, we get that
\(5-y-y=\left(5-y-1\right)+y-1\\\)
This simplifies to
\(5-2y=3\)
Now, for this equation, we get that y is equal to 1.
Thus, subsituting this value into x, we find that
\(x=5-1=4\)
Thus, the answers for the equation are
\(x=4,\:y=1\)
So our final answer is \((4, 1)\)
Thanks! :)
