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elena-s [515]
4 years ago
9

Solve the system using substitution.

Mathematics
2 answers:
salantis [7]4 years ago
5 0
The answer is:  [B]:  (13, -5)  .
______________________________________________________
Explanation:  Using Substitution:
______________________________________________________
   y = 8 − x ;

   7 = 2 − y ;
___________________________________
Solve for "x" and "y" using using substitution;
_________________________________________

Take the second equation given:
____________________________________________
    7 = 2 − y ; 

And considering the first equation given: " y = 8 − x " ;
_________________________________________________
Substitute the value: "8 − x"  for (the value of "y" in the first equation given), in order to solve for "x" ;
_________________________________________________
   7 = 2 − y ; 
________________________________________

   7 = 2 −  8  − x ;
__________________________________________    
   7 = -6 − x ;   
__________________________________________
Add  "6" to EACH side of the equation:
__________________________________________
   7 + 6 =  -6 − x + 6 ;
__________________________________________
   to get:  13 =  -x  ;
__________________________________________
      13 =  -x  ;  ↔   -x  = 13 ; ↔  -1 x  = 13 ;
___________________________________________
   Divide EACH side of the equation by "-1 " ;  to isolate "x" on one side of the equation; and to solve for "x" ;
___________________________________________
        -1 x / -1  = 13 / -1 ;
___________________________________________
          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; 
___________________________________________
Nonetheless, we shall continue.
___________________________________________
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:
__________________________________________
     y = 8 − x ;
____________________________________________
     y = 8 − 13 ;
____________________________________________
     y = -5 .
_____________________________________________
So, we have x = 13; and y = -5; or write as: (13, -5) .   This solution corresponds directly which answer choice: [B]:
__________________________________________________
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:
_____________________________________________
  7 = 2 − y ;
_____________________________________________
  7 =?  2 −  (-5)  ?? ; 
 _____________________________________________
 7 =?   2 +  5 ? ? Yes !
______________________________________________
shtirl [24]4 years ago
3 0
Y=8-x
7=2-(8-x)
7=2-8+x
7=-6+x
13=x
y=8-13
y=-5
B.(13,-5)
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