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Find the ordered pair \((x,y)\) if \(\begin{align*} x+y&=(5-x)+(5-y),\\ x-y&=(x-1)+(y-1). \end{align*}\)

 Jan 9, 2019
 #1
avatar+15350 
+2

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)

 Jan 9, 2019
 #2
avatar+94526 
+1

Thanks, EP....Here's another way

 

Just add the equations and we get that

 

2x  = 4 + 4

2x = 8

x = 4

 

Sub this back into the first equation to find y

 

4 + y  = ( 5 - 4) + ( 5 - y)

 

4 + y   =  6 - y

2y = 2

y = 1

 

 

cool cool cool

 Jan 9, 2019

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