Question

Solve the system using substitution.

Answer 1

The answer is:  [B]:  (13, -5)  .
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Explanation:  Using Substitution:
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   y = 8 − x ;

   7 = 2 − y ;
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Solve for "x" and "y" using using substitution;
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Take the second equation given:
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    7 = 2 − y ; 

And considering the first equation given: " y = 8 − x " ;
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Substitute the value: "8 − x"  for (the value of "y" in the first equation given), in order to solve for "x" ;
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   7 = 2 − y ; 
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   7 = 2 −  8  − x ;
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   7 = -6 − x ;   
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Add  "6" to EACH side of the equation:
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   7 + 6 =  -6 − x + 6 ;
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   to get:  13 =  -x  ;
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      13 =  -x  ;  ↔   -x  = 13 ; ↔  -1 x  = 13 ;
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   Divide EACH side of the equation by "-1 " ;  to isolate "x" on one side of the equation; and to solve for "x" ;
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        -1 x / -1  = 13 / -1 ;
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          x  =  13 .  At this point, the only answer choice that can be correct is answer choice: "[B]: (13, -5)" ; since it is the only answer choice given with a solution of x = 13; 
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Nonetheless, we shall continue.
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Now that we have the solution for "x";  "x = 13";  We shall plug this value into, or "SUBSTITUTE" this value, "13", for "x", into the first equation given, " y = 8 − x " ;  to find the value of  "y"  ; as follows:
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     y = 8 − x ;
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     y = 8 − 13 ;
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     y = -5 .
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So, we have x = 13; and y = -5; or write as: (13, -5) .   This solution corresponds directly which answer choice: [B]:
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Also, to confirm, let us plug in our solved value for "y", which is "-5" ; into our second equation, to see if the equation holds true:
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  7 = 2 − y ;
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  7 =?  2 −  (-5)  ?? ; 
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 7 =?   2 +  5 ? ? Yes !
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Answer 2

Y=8-x
7=2-(8-x)
7=2-8+x
7=-6+x
13=x
y=8-13
y=-5
B.(13,-5)