Question

The sum of two numbers is 12. If one number is subtracted from the other, the result is 0. Find the numbers.

Answer 1

a-b = 0

if you were to solve for "a", what would that look like?

Answer 2

-b=0-a

Answer 3

and if you multiply both sides by -1, what would that look like?

Answer 4

-1(-b)=(-1)0-a

Answer 5

ok, and if we expand that, what's -1 * -b?

Answer 6

1b

Answer 7

so -1 * -a will be 1a
1a = a
1b = b
thus
b = a

Answer 8

so we know about this 2 numbers is that

a + b = 12
a - b = 0

we also know now that, b = a
so if I were to rewrite the 1st equation with b = a in mind, it'd look like
a + b = 12
OR
a + (a) = 12

a + a = 2a, thus

2a = 12

what if we divide both sides by 2?

Answer 9

a=6

Answer 10

hmm, low and behold! a = 6
so if I were to use that in the 1st equation
let's see

a + b = 12
OR
6 + b = 12
# substracting 6 from each side

b = 12 -6 =6
b = 6

Answer 11

well, keep in mind that we knew that b = a, if a = 6, then b = 6 too anyway :)

Answer 12

so let's check that
a + b = 12
a - b = 0

6 + 6 = 12
6 - 6 = 0

Answer 13

....you made that so much easier than i thought it was. ugh. thank you! :)

Answer 14

yw