Question

5x-2y=2 y x+2y=2

x+2y=1 y -3x+y=-10

x+4y=1 y 2x+y=5​

Answer 1

Verified answer

Respuesta

1)

5X - 2Y = 2 Ecuacion 1

X + 2Y = 2 Ecuacion 2

En ecuacion 1:

5X - 2Y = 2

5X = 2 + 2Y (Dividimos entre 5)

X = (2 + 2Y)/5

X = 2/5 + 2Y/5

En la ecuacion 2:

X + 2Y = 2

X = 2 - 2Y

Ya tengo X = X

X = 2/5 + 2Y/5

X = 2 - 2Y

2/5 + 2Y/5 = 2 - 2Y

2Y/5 + 2Y = 2 - 2/5

Hagamos por aparte:

2Y/5 + 2Y = 2Y/5 + 2Y/1 = [2Y + 5(2Y)]/5 = [2Y + 10Y]/5 = 12Y/5

2 - 2/5 = 2/1 - 2/5 = [5(2) - 2]/5 = [10 - 2]/5 = 8/5

12Y/5 = 8/5

12Y = 5(8)/5

12Y = 8

Y = 8/12

Y = 2/3

Reemplazamos el valor de Y en X = 2 - 2Y

X = 2 - 2(2/3)

X = 2 - 4/3

2 - 4/3 = 2/1 - 4/3 = [3(2) - 4]/3 = (6 - 4)/3 = 2/3

X = 2/3

Rta: X = 2/3; Y = 2/3

2)

2X + 3Y = 2 Ecuacion 1

-6X + 12Y = 12 Ecuacion 2

En ecuacion 1:

2X + 3Y = 2

2X = 2 - 3Y (Divido entre 2)

X = (2 - 3Y)/2

X = 2/2 - 3Y/2

X = 1 - 3Y/2

En ecuacion 2:

-6X + 12Y = 12

12Y - 12 = 6X (Divido entre 6)

(12Y - 12)/6 = X

12Y/6 - 12/6 = X

2Y - 2 = X

Ya tengo X = X:

X = 1 - 3Y/2

X = 2Y - 2

1 - 3Y/2 = 2Y - 2

1 + 2 = 2Y + 3Y/2

3 = 2Y + 3Y/2

Hagamos aparte:

2Y + 3Y/2 = [2(2Y) + 3Y]/2 = [4Y + 3Y]/2 = 7Y/2

3 = 7Y/2

7Y = 3(2)

7Y = 6

Y = 6/7

Ahora reemplazo el valor de Y = 6/7 en: 2Y - 2 = X

X = 2Y - 2

X = 2(6/7) - 2

X = 12/7 - 2

12/7 - 2 = [12 - 2(7)]/7 = [12 - 14]/7 = -2/7

X = -2/7

Rta: X = -2/7; Y = 6/7

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