Question

Resuelva por cualquiera de los 3 métodos estas ecuaciones

a. 12(x + 2y) – 8(2x +y) = 2(5x –6y) Y 20(x-4y) = --10
b. 5x –3y = 11 Y 4x + y = 2

Answer 1

a.

12(x + 2y) – 8(2x +y) = 2(5x –6y)

12x + 24y - 16x - 8y = 10x - 12y

12x - 16x - 10x + 24y - 8y + 12y = 0

12x - 26x + 36y - 8y = 0

-14x + 28y = 0

20(x-4y) = -10

20x - 80y = -10

Método de sustitución

-14x + 28y = 0 Ec1

20x - 80y = -10 Ec2

x2 = -10 + 80y/20

-14 (-10 + 80y/20) + 28y = 0

-14 (-10 + 80y) = 20 (-28y)

140 - 1120y = -560y

-1120y + 560y = -140

(-) -560y = -140

560y = 140

y = 140/560

y = 1/4

-14x + 28y = 0 Ec1

-14x + 28(1/4) = 0

-14x + 7 = 0

(-) -14x = -7

14x = 7

x = 7/14

x = 1/2

20x - 80y = -10 Ec2

20x - 80 (1/4) = -10

20x - 20 = -10

20x = -10 + 20

20x = 10

x = 10/20

x = 1/2

R// x = 1/2 ; y = 1/4

Comprobación

-14x + 28y = 0 Ec1

-14 (1/2) + 28 (1/4) = 0

-14/2 + 28/4 = 0

-7 + 7 = 0

0 = 0

20x - 80y = -10 Ec2

20 (1/2) - 80 (1/4) = -10

20/2 - 80/4 = -10

10 - 20 = -10

-10 = -10

b.

Método de igualdad

5x –3y = 11 Ec1

4x + y = 2 Ec2

x1 = 11 + 3y/5

x2 = 2 - y/4

11 + 3y 2 - y

_____ = _____

5 4

4 (11 + 3y) = 5 (2 - y)

44 + 12y = 10 - 5y

12y + 5y = 10 - 44

17y = -34

y = -34/17

y = -2

5x –3y = 11 Ec1

5x - 3 (-2) = 11

5x + 6 = 11

5x = 11 - 6

5x = 5

x = 5/5

x = 1

4x + y = 2 Ec2

4x + (-2) = 2

4x - 2 = 2

4x = 2 + 2

4x = 4

x = 4/4

x = 1

x = 1 ; y = -2

Comprobación

5x –3y = 11 Ec1

5(1) - 3(-2) = 11

5 + 6 = 11

11 = 11

4x + y = 2 Ec2

4(1) + (-2) = 2

4 - 2 = 2

2 = 2

Espero haberte ayudado. Suerte en los estudios ≧◠◡◠≦.