Por pedido de la usuaria respondemos con Método de igualación
A)m+3n=7
3m+n=7
primer paso = despejamos la misma variable en las dos ecuaciones
m + 3n = 7 → m = 7 - 3n
3m + n = 7 → 3m = 7 - n → m = 7/3 - 1n/3
segundo paso= ahora igualamos las m
m = m
7 - 3n = 7/3 - 1n/3
7 - 7/3 = - 1n/3 + 3n juntamos las n y resolvemos
21/3 - 7/3 = - 1n/3 + 9n/3 sacamos comun denominador para restar
14/3 = 8n/3 despejamos n
14/3 : 8/3 = n
7/4 = n
tercer paso = reemplazamos en cualquier ecuación para poder hallar m
m = 7 - 3n
m = 7 - 3(7/4)
m = 7 - 21/4
m = 28/4 - 21/4
m = 7/4
Conjunto de solución (7/4;7/4)
B) 4(2x-y)=16
3x+5y=8
4(2x - y) = 16 → 2x - y = 4 → 2x - 4 = y
3x + 5y = 8 → 5 y = 8 - 3x → y = 8/5 - 3x/5
ahora igualamos
2x - 4 = 8/5 - 3x/5
2x + 3x/5 = 8/5 + 4
10x/5 + 3x/5 = 8/5 + 20/5
13x/5 = 28/5
x = 28/5 : 13/5
x =28/13
y = 2x - 4
y = 2.28/13 - 4
y = 56/13 - 4
y = 56/13 - 52/13
y = 4/13
C) 8a- 4b=16
5-3a = 3(b-2a)
8a - 4b = 16 → 8a = 16 + 4b → a = 2 + 2b
5 - 3a = 3b - 6a → -3a + 6a = 3b - 5 → 3a = 3b - 5 → a = b - 5/3
a = a
2 +2b = b - 5/3
2 +5/3 = b - 2b
6/3 + 5/3 = - b
11/3 = - b
- 11/3 = b
a = 2 +2b
a = 2 + 2(-11/3)
a = 2 - 22/3
a = 6/3 - 22/3
a = - 16/3
Conjunto de solución a = - 16/3 b = -11/3
D) 3(m+n)= - 4
m-n = - 2
3(m + n) = - 4 → m +n = - 4/3 → m = - 4/3 - n
m - n = - 2 → m = - 2 + n
m = m
- 4/3 - n = - 2 +n
- 4/ 3 + 2 = n + n
2/3 = 2n
2/3 : 2 = n
1/3 = n
m= - 2 + 1/3
m = - 5/3
Conjunto de solucion m = - 5/3, n = 1/3
E)3(a+2b)=4a
7b-4(a+3b)=9b-3
3 (a +2b) = 4a → 3a + 6b = 4a → 6b = a
7b - 4(a + 3b) = 9b - 3 → 7b - 4a - 12b = 9b - 3→ - 14b + 3 = 4a → -14b/4 + 3/4 = a
a = a
6b = - 14b/4 + 3/4
6b + 14b/4 = 3/4
19b/2 = 3/4
b = 3/4 : 19/2
b = 3/38
a = 6b → a = 9/19
F)1/x-10/y=6 → 1/x = 6 + 10/y→ 1/(6 +10/y) = x
2/x-5/y=2 → 2/x = 2 + 5/y → 2/(2+ 5y) = x
1/(6 + 10/y) = 2/(2 +5y)
1 (2 + 5y) = 2 (6 +10y)
2+ 5y = 12 + 20 y
2 - 12 = 20y - 5 y
- 10 = - 15y
- 10/-15 = y → 2/3 = y
x = 1 /(6 +10(2/3))
x = 1 / (38/3)
x = 3 /38
N)m/2-n/6=1
m/3-n/2=-1
m/2 - n/6 = 1 → m/2 = 1 + n/6 → m = 2 + n/3
m/3 - n/2 = - 1 → m/3 = -1 + n/2 → m = - 3 + 3n/2
2+n/3 = - 3 + 3n/2
2 + 3 = 3n/2 - n/3
5 = 9n/6 - 2n/6
5 = 7n/6
5 : 7/6 = n
30/7 = n
m = 2 + n/3
m = 2 + (30/7: 3)
m = 2+10/7
m = 24/7
conjunto de solución m = 24/7 n = 30/7
resolver los siguientes sistemas
A)1/2x-3/5y=-1
2/3x+3/4y=2
1/2x - 3/5y = - 1→ - 3/5y = - 1 - 1/2x → y = 5/3 + 5/6x
2/3x + 3/4y = 2 → 3/4y = 2 - 2/3x → y = 8/3 - 8/9x
5/3 + 5/6x = 8/3 - 8/9x
5/3 - 8/3 = 8/9x - 5/6x
- 3/3 = 1/18x
- 1 : 1/18 = x
- 18 = x
y = 5/3 + 5/6x→ y = 5/3 + 5/6(-18) → y = 5/3- 15→ y = - 40/3
Conjunto de solucion (-18, -40/3)
B)0,07x+0,3y=0,2
0,8x+0,25y=0,5
0,3y = 0,2 - 0,07x → y = 2/3 - 7/30x
0,8x + 0,25y = 0,5 → 0,25y = 0,5 - 0,8x → y = 2 - 16/5x
2/3 - 7/30x = 2 - 16/5x
- 7/30x + 16/5x = 2 - 2/3
89/30x = 4/3
x = 4/3 : 89/30
x = 40/89
y = 2 - 16x/5
y = 2 - 16(40/89)/5
y = 2 - 128/89
y = 50/89
Conjunto de solucion (40/89, 50/89)
espero que te sirva,salu2!!!!
