ayudenme en estos ejercicios xfa es urgente

resolucion de ecuaciones lineales mediante el metodo de suma y resta

1)

0,1x-0,2y=6

2,4x+1,2y=-3

2)

4x-2y=6

2x+2y=4

3)

3x+5y=1

6x+10y=2

4)

1/2x+4/3y=4

3/8x-1/3y=2

5)

x+y=4

5x+10y=9

6)

4x+5y=9

x-3y=-2

7)

3x+4y=1

6x+8y=2

8)

2x+6y=5

x+3y=-3

9)

0,5x +0,3y=1,2

1,5x+y=4

10)

1/2x+3/4y=2

x-2y=1

1

Respuestas

2013-03-17T23:47:50+01:00

Para aplicar el método por igualación debemos despejar en ambas ecuaciones del sistema la misma incógnita:
1) 
5x + 7y = -1
x + 3y = -5
5x + 7y = -1 ==> 5x = -1 -7y ==> x = (-1-7y)/5
x + 3y = -5 ==> ..........................x = -5 -3y
como x = x entonces sus segundos miembros también son iguales:
(-1 -7y)/5 = -5 -3y
-1 - 7y = 5(-5 -3y)
-1 -7y = -25 -15y
-7y +15y = -25 +1
8y = -24
y = -24/8
y = -3
reemplazamos y = -3 en cualquiera de las ecuaciones:
5x + 7y = -1
5x +7(-3) = -1
5x - 21 = -1
5x = -1 + 21
x = 20/5
x = 4
verificamos reemplazando los valores hallados en cualquiera de las ecuaciones:
x + 3y = -5
4 + 3(-3) = -5
4 - 9 = -5
-5 = -5 cqd.
2) 
2x + y = 11==> 2x = 11 -y ==> x = (11-y)/2
x + 3y = 18......................==> x = 18-3y

(11-y)/2 = 18 - 3y
11-y = 2(18 -3y)
11-y = 36 - 6y
-y +6y = 36 -11
5y = 25
y = 5

2x + y = 11
2x +5 = 11
2x = 11-5
x = 6/2
x = 3
---------------------------------------…
3)
-x + y = 5 ==> -x = 5 - y ==> x = -5 +y
x + y = 1 .......................==> x = 1 -y

-5 + y = 1-y
y +y = 1 +5
2y = 6
y = 6/2
y = 3

x+y = 1
x +3 = 1
x = 1 -3
x = -2
---------------------------------------…
4) 
4x - 5y = -4 ==> 4x = -4 +5y ==> x = (-4 +5y)/4
3x - 2y + 3 = 0 ==> 3x = -3 +2y ==> x = (-3 +2y)/ 3

(-4+5y)/4 = (-3+2y)/ 3
3 (-4 +5y) = 4(-3 +2y)
-12 + 15y = -12 +8y
15y -8y = -12 +12
7y = 0
y = 0

4x - 5y = -4
4x - 5*0 = -4
4x - 0 = -4
4x = -4
x = -1
---------------------------------------…
5) 
3x + 4y = 8 ==> 3x = 8 -4y ==>......x = (8 -4y) /3
-9y + 8x = 77 ==> 8x = 77 +9y ==> x = (77+9) /8

(8-4y)/3 = (77+9y)/8
8(8-4y) = 3(77+9y)
64 -32y = 231 + 27y
-32y - 27y = 231 - 64
-59y = 167
y = 167/(-59)
y = -167/59

3x + 4y = 8
3x +4*(-167/59) = 8
3x - 668/59 = 8
3x = 8 + 668/59
x = [(472 + 668)/59]/3
x = 1140/177
x = 380/59
---------------------------------------…
6) 
3x - 4y = 6 ==> -4y = 6 -3x ==> ............4y = +3x -6 ==> Y =(3/4x -6/4) ==> y = 3/4x - 3/2 
8y - 6x + 4 = 0 ==> 2(4y -3x +2) =0 ==> 4y = +3x -4==> y = (3/4x - 4/4)==> y = 3/4x -1
como puedes apreciar la pendiente en ambos casos (m = 3/4) es la misma ==> el sistema es incompatible porque las rectas (si las graficas) son paralelas...
---------------------------------------…
7) 
7y - 9x = 8 ==> 7y = 8 +9x ==> y = (9x +8) /7
y - 12 - 3x = 0 ==>................... y = 3x +12

(9x +8)/7 = 3x +12
9x +8 = 7(3x +12)
9x +8 = 21x +84
9x -21x = 84 -8
-12x = 76
x = 19/(-3)
x = -19/3

y =(9x +8) /7
y = [9*(-19/3)+8] / 7
y = (3*(-19) + 8)/7
y = (-57+8)/7
y = -49/7
y = -7
---------------------------------------…
8) 
x + 2y - 15 = 0 ==> x = -2y + 15
x + 7 = 2y ==> ......x = 2y -7

-2y +15 = 2y -7
-2y -2y = -7 -15
-4y = -22
y = 22/4
y = 11/2

x + 7 = 2y 
x = 2*(11/2) -7
x = 11-7
x = 4
---------------------------------------…
9) 
10x + 18y = -11 ==> 10x = -11 -18y ==> x = (-11 -18y) /10
16x - 9y = -5 ==> 16x = -5 +9y ==>........x = (-5 +9y)/16

(-11 -18y) /10 = (-5 +9y)/16
16(-11-18y) = 10(-5 +9y)
-176 - 288y = -50 + 90y
-288y -90y = -50 +176
-378y = 126
y = 126/(-378)
y = -1/3

10x + 18y = -11
10x +18*(-1/3) = -11
(30x - 18)/3 = -11
30x -18 = -11*3
30x = -33 + 18
x = -15 / 30
x = -1/2
---------------------------------------…
10) 
32x - 25y = 13 ==> 32x = 13 +25y ==> x = (13+25y)/32
15y + 16x = 1 ==> 16x = 1 - 15y ==> x = (1-15y)/16

(13+25y) /32 = (1-15y) /16
(13+25y ) /2 = (1-15y)
13 +25y = 2(1-15y)
13 +25y = 2 -30y
25y +30y = 2 -13
55y = -11
y = -11/55
y = -1/5

15y + 16x = 1
15(-1/5) +16x = 1
-3 +16x = 1
16x = 1 +3
16x = 4
x = 4/16
x = 1/4
---------------------------------------…
Aclaro que de aquí en adelante debí reducir la explicación dado que no me daba el espacio para explayarme....
11)
-15y - 10x = -30 ==> x = (6-3y)/2 
10x - 8y = -16 ==> x = (-8-4y)/5

(6-3y)/2 = (-8+4y)/5
y = 36/23

10x - 8y = -16
10x -8(36/23) = -16
x = -8/23
---------------------------------------…
12) 
3x + 2y = -6 ==> 2y = -6 -3x ==> y = (-6-3x) /2
-6x + 2y = -6 ==> 2y = -6 +6x ==> y = (-6 +6x) /2

(-6 -3x) /2 = (-6+6x)/2
x = 0

3x +2y = -6
3*0 +2y = -6
y = -3
---------------------------------------…
13) 
5x + 3y = 6 ==> 5x = 6 -3y ==> x = (6-3y) /5
2x - 4y = 5 ==> 2x = 5 +4y ==> x = (5+4y)/2

(6-3y)/5 = (5+4y)/2
y = -1/2

5x + 3y = 6
x = 3/2
---------------------------------------…
14)
-13y + 163 = -11x ==> -13y = -11x -163 ==> y = (11x +163) /13
7y - 94 = 8x ==>7y = 8x +94 ==> ...............y = (8x +94) /7

(11x +163) /13 = (8x +94) /7
x = 81/(-27)
x = -3

7y - 94 = 8x
y = 10
Suerte!!!!!!!!!!!!!!!!!!!!!!!