Find the ordered pair \((x,y)\) if:

\( \begin{align*} x+y&=(5-x)+(5-y),\\ x-y&=(x-1)+(y-1). \end{align*}\)

onyulee Jul 3, 2024

#2**+2 **

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! :)

NotThatSmart Jul 3, 2024