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avatar+36 

Find the ordered pair \((x,y)\) if:

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

 Jul 3, 2024
 #1
avatar+867 
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Solving the system, we get (x,y) = (3,2).

 Jul 3, 2024
 #2
avatar+1265 
+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! :)

 Jul 3, 2024

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