Find the ordered pair \((x,y)\) if \(\begin{align*} x+y&=(5-x)+(5-y),\\ x-y&=(x-1)+(y-1). \end{align*}\)
Simplify the first eq:
x+y = 5-x+5-y
2x +2y =10
Simplify the second eq:
x-y=x-1+y-1
-2y = -2
y =1 Sub this into the first equation 2x+2(1)=10 2x+2=10 x = 4 ordered pair = (4,1)