20 points

using the substitution method, solve the following equations.
1.) m+n=5
m-n=3
2.) y=3x-7
6x-2y=12
3.) 5x+2y=7
y=x+7
4.) y+2x=7
14 - 4x=2y
5.) y=4x+6
5x-y=6

1.) m + n = 5
m - 3 = n

m + m - 3 = 5
2m - 3 = 5
2m = 8
m = 4

m + n = 5
4 + n = 5
n = 1

Therefore m =4 and n =1

2.) I don't think this one can be done because:
6x - 2(3x - 7) = 12
6x - 6x + 14 = 12
0x + 14 = 12
0x = - 2

3.) 5x + 2(x + 7) = 7
5x + 2x + 14 = 7
7x + 14 = 7
7x = - 7
x = - 1

y = x + 7
y = - 1 +7
y = 6

Therefore x = - 1 and y = 6

4.) I don't think this one can be done either because:
14 - 4x = 2y
Is the same as:
7 - 2x = y
Which is the same as the first equation. You then get 0x because if you substitute y in:
7 - 2x + 2x =7
7 = 7

5.) y = 4x + 6
5x - 4x + 6 = 6
x +6 = 6
x = 0

y = 4x + 6
y = (4x0) + 6
y = 6

Therefore x = 0 and y = 6

Definitely