Question

A)4m+3n=12
   3m-2n=-8
B)2p-3q=5
   3p+2q=-5                                         metodo de igualacion
C)7a-2b=9
   2a-5b=7
D)m+3n=7
   3m+n=7
E)3p+4q=6
   2p+3q=5

Answer 1

A)4m+3n=12
   3m-2n=-8
Despejamos
4m + 3n = 12 → 4m = 12 - 3n → m = 12/4 - 3n/4→m = 3 - 3n/4
3m - 2n = - 8 → 3m = - 8 + 2n →m = -8/3 + 2n/3
igualamos
3 - 3n/4 = - 8/3 + 2n/3
3 + 8/3 = 2n/3 + 3n/4       buscamos comun denominador para sumar
9/3 +8/3 = 8n/12 + 9n/12
17/3 = 17n/12
17/3 : 17/12 = n
4 = n
hallamos m
m = 3 - 3n/4
m = 3 - 3(4)/4
m = 3 - 12/4
m = 3 - 3
m = 1
  Conjunto de solución  m = 0  n = 4
B)2p-3q=5
   3p+2q=-5      
2p - 3q = 5 → 2p = 5 + 3q → p = 5/2 + 3q/2
3p + 2q = - 5 → 3p = -5 - 2q →p = -5/3 - 2q/3
5/2 + 3q/2 = - 5/3 - 2q/3
5/2 + 5/3 = - 2q/3 - 3q/2
15/6 + 10/6 = -4q/6 - 9q/6
25/6 = - 13q/6
25/6 : - 13/6 = q
- 25/13 = q

p = 5/2 + 3q/2
p = 5/2 + 3(-25/13) /2
p = 5/2 - 75/26
p = - 5/13
Conjunto de solución      p = - 5/13    q = - 25/13
       
C)7a-2b=9
   2a-5b=7
7a - 2b = 9 → 7a = 9 + 2b → a = 9/7 +2b/7
2a - 5b = 7 → 2a = 7 + 5b → a = 7/2 + 5b/2
9/7 + 2b /7 = 7/2 + 5b/2
9/7 - 7/2 = 5b/2 - 2b/7
- 31/14 = 31b/14
-31/14 : 31/14 = b
 - 1 = b
a = 9/7 +2b/7
a = 9/7 +2(-1)/7
a = 9/7 - 2/7
a = 7/7
a = 1
Conjunto de solución a = 1          b = -1 

D)m+3n=7
   3m+n=7
m + 3n = 7 → m = 7 - 3n
3m + n = 7 →m = 7/3 - n /3
7 -3n = 7/3 - n/3
7 - 7/3 = -n/3 + 3n
14/3 = 8n/3
14/3 : 8/3 = n
7/4 = n

m = 7 - 3n
m = 7 - 3(7/4)
m = 7 - 21/4
m = 7/4
Conjunto de solución   m = 7/4      n = 7/4

E)3p+4q=6
   2p+3q=5
3p + 4q = 6 → 3p = 6 - 4q →p = 6/3 - 4q/3
2p + 3q = 5 → 2p = 5 + 3q → p = 5/2 - 3q/2
2 - 4q/3 = 5/2 - 3q/2
2 - 5/2 = - 3q/2 + 4q/3
- 1/2 = -1q/6
-1/2 : -1/6 = q
3 = q
p = 6/3 - 4q/3
p = 6/3 - 4(3)/3
p = 2 - 4
p = -2
Conjunto de solución    p = - 2      q = 3

espero que te sirva, salu2!!!!