SOLUTION: 13-y=17 solve for y by dividing each side by -1

Question 1171641: 13-y=17 solve for y by dividing each side by -1
Found 2 solutions by Boreal, Theo:
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
after dividing by -1
-13+y=-17
y=-4.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
13 - y = 17
divide both side by -1 to get:
(13 - y) / -1 = 17 / -1
simplify to get:
-13 + y = -17
add 13 to both sides of the equation to get:
y = -17 + 13 = -4

if you did not divide each side by -1, you would have gotten:
13 - y = 17
add y to both sides of the equation and subtract 17 from both sides of the equation to get:
13 - 17 = y
solve for y to get:
y = -4.

it appears that the value of y is unchanged.

in 13 - y = 17, replace y with - 4 to get:
13 - -4 = 17 which becomes 13 + 4 = 17 which becomes 17 = 17.

in -13 + y = -17, replace y with -4 to get:
-13 - 4 = -17 which becomes -17 = -17

the final value has been changed from 17 to -17, but the equality has been preserved.

17 = 17 and -17 = -17.

this is one of the rules of solving equations.
if you multiply both sides of the equation by the same amount, the equality is preserved.

since division is a form of multiplication, this applies to division as well.

you could have divided by any number and the equality would have been preserved.

for example, if you divided by -13, you would have gotten:

13 - y = 17 becomes:
13/-13 - y/-13 = 17/-13
you would add y/-13 to both sides of the equation and you would subtract 17/-13 from both sides of the equation to get:
13/-13 - 17/-13 = y/-13
you would multiply both sides of the equation by -13 to get:
13 - 17 = y
this would result in y = -4

if you solved the original equation without dividing by -13, you would have gotten.
13 - y = 17
add y to both sides and subtract 17 from both sides to get:
13 - 17 = y
solve for y to get:
y = -4.

if you replaced y with -4 in the original equation, you would have gotten:
13 - -4 = 17 which would have resulted in:
17 = 17.

if you replaced y with -4 in the equations that was divided by -13 on both sides, you would have gotten:
13/-13 - y/-13 = 17/-13 becomes:
13/-13 - -4/-13 = 17/-13 which becomes:
13/-13 + 4/-13 = 17/-3 which becomes:
17/-13 = 17/-3
the result was different but the equality was preserved.

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