Can someone break this down for me?

1. Look at the two equations to see which one is "simpler"
2. I would choose the second equation, since m can be isolated easily
3. Isolate m in the second equation by adding 6n to both sides
4. You should get m=6n+22 as the new second equation
5. "Substitute" your new second equation into the first one, since you have found out what m equals.
6. You should get 5(6n+22)+n=17
7. Distribute the 5 to the part in the parenthesis
8. You should get 30n+110+n=17
9. Simplify by combining like terms
10. You should now have 31n=-93
11. Divide both sides by 31 to isolate n
12. n=-3
13. Substitute you new value of n into either of the two original equations to find m.
14. If I plug it into the first of the two original equations, I get 5m+(-3)=17
15. Simplify to get 5m=20
16. m = 4
17. From before, n = -3

1st equation (n):
5m + n = 17
n = 17 - 5m

2nd equation (n):
m - 6n = 22
6n = m - 22
n = (m - 22)/6

Value of m:
6(17 - 5m) = m - 22
102 - 30m = m - 22
31m = 124
m = 4

Value of n (1st equation):
= 17 - 5(4)
= 17 - 20
= - 3

Answer: m = 4, n = - 3

Proof (1st equation):
5(4) + (- 3) = 17
20 - 3 = 17
17 = 17

Proof (2nd equation):
4 - 6(- 3) = 22
4 + 18 = 22
22 = 22

first pick an equation and solve for a variable (it doesn't matter which) i pick the first one and "n" because that is the easiest

5m+n=17
n=17-5m
then just plug that in for 'n' in the other equation
m-6n=22
m-6(17-5m)=22
m-102+30m=22
31m=124
m=4
plug that in to either of the first given equations...
5m+n=17
5(4)+n=17
20+n=17
n=-3

m=4 and n=-3

good luck on the test!

5m + n = 17
m - 6n = 22


5m + n = 17
n = 17 - 5m

m - 6n = 22
m - 6(17 - 5m) = 22
m - 102 + 30m = 22
m + 30m = 102 + 22
31m = 124
m = 124/31
m = 4

m - 6n = 22
4 - 6n = 22
-6n = 22 - 4
n = 18/-6
n = -3

∴ m = 4 , n = -3

5m+n=17....1
m-6n=22.....2

m = 6n + 22...3

5(6n +22) +n = 17

30n + 110 +n = 17
31n = 17 - 110
31n = -93
n = -93/31
put n = -3 into 3

m = 6n + 22
m = 6(-3) + 22 = -18 + 22 = 4

5m+n=17
m-6n=22==>-5m+30n=-110====>31n=-93==>
n=-3,m=4

There are a lot of ways you can solve this type of problem: Elimination, Substitution, Kramer's rule... and more. But I'm just going to use substitution because its easier to write in this box:

To use substitution first you mus solve for one variable. Lets solve for n in the 1st equation:

5m+n=17 (subtract 5m from both sides)
n=17-5m

Now that we know what n equals, we plug that in to the 2nd equation:

m-6n=22
m-6(17-5m)=22 (Multiply 6 by 17 and 5m)
m-102+30m=22 (Add all like terms)
31m-102=22 (Add 102 to both sides)
31m=124 (divide both sides by 31)
m=4

Now we have an answer for m. So now we plug that in for m on one of the previous equations. We could use one of the original 2, but it would be easier to use n=17-5m

n=17-5m (plug in the value for m)
n=17-5(4) (multiply)
n=17-20
n=-3

And that is your answer. You can check it by plugging these values into either of the original equations.

N= -3
M=4

5m + n = 17
m - 6n = 22 --> m = 22 + 6n

5(22 + 6n) + n = 17
110 + 30n + n = 17
31n = -93
n = -3
--> 5m - 3 = 17
5m = 20
m = 4