Question

a) 2x + y = 1
3x + 2y1
b) -10 x + 3y= 42
5x + y=-11
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Answer 1

Respuesta:

EJERCICIO A

2x+y=1

3x+2y=1

X = 1

Y = -1

EJERCICIO B

-10 x + 3y= 42

5x + y=-11

X = -3

Y = 4

Explicación paso a paso:

EJERCICIO A

2x+y=1

3x+2y=1

DESPEJANDO x DE LAS DOS ECUACIONES

X = (1-Y)/2.....(1)

X = (1-2Y)/3....(2)

IGUALANDO AMBAS NUEVAS ECUACIONES (1) Y (2)

(1 - Y)/2 = (1 - 2Y)/3

(1 - Y)3 = (1 - 2Y)2

3 - 3Y = 2 - 4Y

4Y - 3Y = 2-3

Y=-1

REEMPLAZANDO EN (1)

X = (1-Y)/2

X = (1-(-1)/2

X = 2/2

X = 1

COMPROBANDO:

2(1) +(-1) = 1

2 - 1 = 1

1 = 1 .... COMPROBADO

3(1) + 2(-1) = 1

3 - 2 = 1

1 = 1 .... COMPROBADO

EJERCICIO B

-10 x + 3y= 42

5x + y=-11

DESPEJANDO x DE LAS DOS ECUACIONES

X = (42-3Y)/(-10).....(1)

X = (-11-Y)/5....(2)

IGUALANDO AMBAS NUEVAS ECUACIONES (1) Y (2)

(42-3Y)/(-10) = (-11-Y)/5

(42-3Y)(5) = (-11-Y)(-10)

210 - 15Y = 110 + 10Y

15Y + 10Y = 210 - 110

25Y = 100

Y = 100/25

Y = 4

REEMPLAZANDO EN (1)

X = (42-3Y)/(-10)

X = (42-3(4))/(-10)

X = 30/-10

X = -3

COMPROBANDO:

-10(-3) + 3(4)= 42

30 + 12 = 42

42 = 42.... COMPROBADO

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

-15 + 4 = -11

-11 = -11 .... COMPROBADO