Could you help me with a math problem?

Question

Solve by either the substitution or the addition-or-subtraction method.

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

Thanks for the help!

Answer 1

Use the substitution method.
Restate the first equation to isolate the "n" term.
n = 2m + 3
Substitute 2m + 3 for n in the second equation:
3m = 2(2m + 3) - 9
Combine like terms:
3m = 4m + 6 - 9
-1m = -3
m = 3
Substitute 3 for m in either equation to solve for n.
n = 9

Answer 2

Otherwise known as the Elimination Method:

3 [ 2m = n - 3 ]
- 2 [ 3m = 2n - 9 ]

then..

6m = 3n - 9
-6m = -4n + 18

adding the two equations...

0 = -n + 9

therefore, n = 9

substituting n = 9 in the first equation...

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

therefore, n = 9 and m = 3

Answer 3

The subsition method:

I'd solve for n in the first equation, so it would be 2m+3=n

Then substitute that into the 2nd equation, so you'd have
3m=2(2m+3)-9

Solving this:
3m=4m+6-9
3m=4m-3
-1m=-3
m=3

Then plug this back into the first equation:
2*3+3=n, or n=9

By addition or subtration, I'd multiply everything in the 1st equation by -2, so your 2 equations would be:

-4m = -2n + 6
3m = 2n -9

Adding these together, you'd get

-1m = -3 (the n's would cancel out)
or m=3

Then stick this into one of the equation (I'll do the 1st)
2*3=n-3
6=n-3
9=n

Either way, you get m=3 and n=9

Answer 4

Substitution: First, you would get one variable on a side by itself.
2m = n - 3
+3 +3
cond equation.
3m = 2(2m + 3) - 9
Next, simplify the second equation by distributing the 2.
3m = 4m + 12 - 9 which becomes 3m = 4m + 3
Then get all the 'm's on one side by subtracting.
3m = 4m + 3
-4m -4m
-m = 3.
Then divide both sides by negative 1 so that the variable is not negative.
m = -3.
Then replace m by -3 in one of the original equations and solve for n.
2(-3) = n -3
Mulitiply the 2 by negative three.
-6 = n - 3
Add three to both sides so that n is by itself.
-6 = n - 3
+3 +3
-3 = n.
The answers are
m = -3
n = -3
Sorry it's so long, I hope it helps.

Answer 5

from the first equation:
n=2m+3
put this into the second equation:

3m=2(2m+3) - 9
3m = 4m +6 -9
m = 3

now use the first equation again:
2(3)= n-3
n=9

Answer 6

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

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

plug back into the first equation
2m=n-3=2*(n-6) = 2n-12
n-3=2n-12
9=n
m=3

Answer 7

solve the top one for n
2m + 3 = n

Now put that in the bottom one.

3m = 2(2m + 3) - 9
3m = 4m + 6 - 9
3m = 4m - 3
-m = -3
m = 3

Now you can find n.
n = 2m + 3 = 2(3) + 3 = 9

Answer 8

n= 2m+ 3
3m= 2(2m + 3) - 9
3m = 4m + 6 - 9
-m = -3
m =3
n = 2*3 + 3
n =6 +3
n=9

or
-4m = -2n + 6
3m = 2n - 9
-------------------
-m =-3
m = 3
9 =2n -9
18 = 2n
9 = n

Answer 9

2m=n-3
n=2m+3-----(1)
3m=2n-9----(2)
sub (1) into (2)

3m=2(2m+3)
3m=4m+6
-m=6
m= -6

sub m=-6 into (1)
n=2m+3
=2(-6)+3
=-12+3
=-9

Answer 10

2M=N-3
3M=2N-9

3{(N-3)/2}=2N-9
3/2N-9/2=2N-9
3/2N-2N=-9+9/2
-N/2=-9/2
N=9

3M=2N-9
M={2(9)-9}/3
M=3