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2 years ago

20 points!!!

1 answer:

4 0

The answer is: {4, 1} .
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Explanation:
________________________________________
Given the equations:
________________________________________
"12x = 54 − 6y ;
"-17x = -62 − 6y ;
_________________________________________
Multiply the second equation (both sides) by "-1" ;
___________________________________________
-1*{-17x = -62 − 6y} ;

to get:

17x = 62 + 6y ;
___________________________________________
{Note: The reason we do this is that we notice the TWO "-6y" values; and by multiplying one of the entire equations by "-1" ; we can change said equation to an equation with a "(+6y)" value; and the "(+6y)" and the "(-6y)" values cancel out to "zero" ; providing an opportunity to isolate "x"; and to solve for "x".}.
___________________________________________
Now, rewrite the two equations:
___________________________________________

12x = 54 − 6y ;
17x = 62 + 6y ;
___________________________________________
↔ Rewrite; and then add the two together:

6y + 62 = 17x
-6y + 54 = 12x
____________________
0 + 116 = 29x ;

↔ 29x = 116 ;

Divide EACH SIDE of the equation by "29" ; to isolate "x" on one side of the equation ; and to solve for "x" ;
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29x / 29 = 116 / 29 ;
________________________________________________
to get:
________________________________________________
x = 4 .
______________________________________________
Now that we have the value for "x" , which is "4" ; let us plug in "4" for "x" for either of the original two equations, to solve for "y". In fact, let us try substituing "4" for "x" ; for BOTH of the two original equations; to see if the value is correct.
_____________________________________________
Our original two given equations are:
_____________________________________________
"12x = 54 − 6y ;

"-17x = -62 − 6y ;
_____________________________________________
Let us start with the first equation:
________________________
" 12x = 54 − 6y " ;
__________________________________
When "x = 4" ; what does "y" equal ?

Plug in "4" for "x" ; to solve for "y" ;

12(4) = 54 − 6y ;

→ 48 = 54 − 6y ;

Subtract "54" from EACH SIDE of the equation;

→ 48 − 54 = 54 − 6y − 54 ;

to get:

→ -6 = -6y ;

→ Divide EACH side of the equation by "-6" ; to isolate "y" on one side of the equation ; and to solve for "y" ;

→ -6/-6 = -6y / -6 ;

to get:

1 = y ; ↔ y = 1 ; So, we have: x = 4, y = 1 ; or, {4, 1}.
______________________________________________
Let us check to see, if the second (orginal equation) holds true when "x = 4" and "y = 1 " ;
______________________________________________
The second "original equation" given is:
______________________________________________
" -17x = -62 − 6y " ;
______________________________________________
→ -17(4) = ? -62 − 6(1) ?

→ -68 = ? -62 − 6 ?

→ -68 = ? -68 ? Yes!
________________________________________________________
The answer is: {4, 1} .
________________________________________________________

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