If m + n = 7 and 2n - 3m = 6, what is the value of 3n - 2m ?

Since m + n = 7 we know m = 7-n. So now we have 2n - 3(7-n) = 6. From this we get n = -3. So now we know m - 3 = 7 so m = 10. So now we have 3(-3) + 2(10) = ? and this comes out as 11

m + n = 7 then m = 7 - n
2n - 3m = 6

substitute m = 7 - n into 2n - 3m = 6
2n - 3m = 6
2n - 3(7 - n) = 6
2n - 21 + 3n = 6
5n - 21 = 6
5n = 27
n = 27/5
n = 5.4

m + n = 7
m = 7 - n
m = 7 - 5.4
m = 1.6

now you have m = 1.6 and n = 5.4
you can find the value of 3n - 2m

3n - 2m
=3(5.4)  - 2(1.6)
= 16.2 - 3.2
= 13