The difference of two numbers is 6. The second number is 9 less than 2 times the first.?

Question

What are the two numbers?

Answer 1

m-n=6
2m-9=n
=m-6
m=3
n=-3

edit
well, i realized there's nowhere in your question mention which is which. either m or n (in my equation) could be the 1st or 2nd number.

actually it's
2m-9=n
AND
6=lm-nl
n=m+-6
2m-9=m+-6
m=9+-6
m=3 or m=15
for m=3, n=-3
for m=15, n=21

so, 2 sets of answers?

(3, -3) and (15, 21)

Answer 2

Okay,

A = B-6 or A = B+6
B=2A-9

so now.....

A must be lower than B.

so the numbers are 15 and 21.

21 - 15 = 6

Let B be 21 and A be 15.

so B (21) is 9 less than 2 times A (30)

which is true. And the difference between the two numbers 21 and 15 is 6.

So 21 and 15 is your answer.

Answer 3

Let m and n be the two numbers

m - n = 6 or m = n + 6

n = 2m - 9

n = 2n + 12 - 9 (substituting from the first equation m)

n - 2n = 3

- n = 3

n = -3

m = + 3

The difference of m - n = 3 - (-) 3 = 6

n = 2m - 9 = 6 - 9 = - 3 as already obtained.

So, - 3 and + 3 are the two numbers.

Answer 4

First (larger number) is F.
Second (smaller number) is S.

The difference (subtract) of two numbers is 6.
F - S = 6

The second number is 9 less than 2 times the first.
S = 2*F - 9

Plug in the second equation into the first equation, to solve for F.
F - S = 6
F - (2*F - 9) = 6 distribute the negative
F - 2*F - (-9) = 6
F - 2*F + 9 = 6
-F + 9 = 6
We can add/subtract/multiply/divide by the same amount on both sides of an equals equation, and still keep the equality. We want to isolate F by itself on one side of the equation, and have it multiplied only by 1.
-F + 9 + F = 6 + F
9 = 6 + F
9 - 6 = 6 + F - 6
3 = F

Now we plug this value for F back into the second equation to find the value of S.
S = 2*F - 9
S = 2*(3) - 9
S = 6 - 9
S = -3

now, to check our work, plug in the found values for F and S back into the first (difference) equation.
F - S = 6
3 - (-3) ?= 6
3 + 3 ?= 6
6 = 6 yea! our answers work.

The numbers are 3 and -3.

Answer 5

Lets say first number x, and second number y.

x-y=6 ................equation 1
y+9=2x ...............equation 2

and x=6+y, right?

substitute x=6+y into equation 2:
y+9=2(6+y)
y+9=12+2y
y-2y=12-9
-y=3
y=-3

then you can use either equation 1 or 2 to find x:
x-(-3)=6
x+3=6
x=6-3
x=3

(-3)+9=2x
2x=6
x=3

Hope that answers your question.

Answer 6

x - y = 6
y = 2x - 9
x - (2x - 9) = 6
-x + 9 = 6
-x = -3
x = 3

3 - y = 6
- y = 3
y = -3

Answer 7

x - y = 6
2x - 9 = y

x - (2x - 9) = 6
- x + 9 = 6
x = 3
y = - 3
The numbers are 3 and - 3.

Answer 8

Let the nos. be A & B.
so, A-B = 6......1
&, B = 2A-9........2
FROM 1, A = B + 6. PUTTING THIS VALUE IN 2
B = 2(B + 6) -9
= 2B + 3
so, B = -3 & SO A = 3

Answer 9

x - y = 6
y = 9-2x or 2x + y = 9

x = 6
2x = 9 or x = 9/2

x = 1 1/2
y = -4 1/2

Answer 10

let the two nos be x & y
then
x-y = 6
and y+9 = 2x
solvin above two equations
x=3
y= -3