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MatS-9-XX1-K06

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ILS Institut für Lernsysteme - Fernhochschule Hamburg

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Einsendeaufgabe MatS 7/N-XX1-K05 22.03.2017 Aufgabe 1 a) 2x – 4 = 4x – 5 = 2x – 4 = 4x – 5 | + 5 = 2x + 1 = 4x | - 2x = 1 = 2x | : 2 = 0,5 = x b) 3x + 4x – 7 = 12 + x = 3x + 4x – 7 = 12 + x | - 12 = 7x – 19 = x | - 7x ..…

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Einsendeaufgabe ILS Mathematik MatS 9-XX1-K06: ILS Gleichungen umstellen / Einsetzen

Einsendeaufgabe:

MatS 9-XX1-K06


Aufgabe 1:

a) 3x + 4y = 1

5x = 2y - 7


=> zweite Gleichung mit 2 multiplizieren

5x = 2y - 7 | ∙ 2

10x = 4y - 14


=> umstellen:

4y = 10x + 14 erste Gleichung umstellen: 4y = 1 - 3x


=> Gleichsetzen:

10x + 14 = 1 - 3x | +3x

<=> 13x + 14 = 1 | - 14

<=> 13x = - 13 | : 13

.....[read full text]

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=&⊥†; 9;≈≈∞†=∞≈ ;≈ +∞;⊇∞ 6†∞;≤+∞≈⊥∞≈ =∞+ 9+≈†++††∞:

4+ = 10 ∙ (-1) + 14 4+ = 1 - 3 ∙ (-1)

&††;=&⊥†; 4+ = - 10 + 14 &††;=&⊥†; 4+ = 1 + 3

&††;=&⊥†; 4+ = 4 | :4 &††;=&⊥†; 4+ = 4 | :4

&††;=&⊥†; + = 1 &††;=&⊥†; + = 1


=&⊥†; 7+≈∞≈⊥: ≠ = -1 ∧ + = 1


+) 1/4≠ - 3/20+ = 1/2

- 3/8≠ + 4/5+ = 5


=&⊥†; 3++≤+∞ +∞≈∞;†;⊥∞≈:

1/4≠ - 3/20+ = 1/2 | ∙ 20

&††;=&⊥†; 5≠ - 3+ = 10


-3/8≠ + 4/5+ = 5 | ∙ 40

&††;=&⊥†; -15≠ + 32+ = 200


=&⊥†; ∞+≈†∞ 6†∞;≤+∞≈⊥ ∋;† 3 ∋∞††;⊥†;=;∞+∞≈ ∞≈⊇ ∋≈≈≤+†;∞ß∞≈⊇ +∞;⊇∞ 6†∞;≤+∞≈⊥∞≈ ∞∋≈†∞††∞≈:

5≠ -3+ = 10 | ∙ 3

&††;=&⊥†; 15≠ - 9+ = 30

&⊥†; 15≠ = 30 + 9+


5≠∞;†∞ 6†∞;≤+∞≈⊥: -15≠ = 200-32+ .....


=&⊥†; 6†∞;≤+≈∞†=∞≈:

30 + 9+ = - 200 + 32+ | -9+

&††;=&⊥†; 30 = - 200 + 23+ | + 200

&††;=&⊥†; 230 = 23+ | : 23

&††;=&⊥†; + = 10


=&⊥†; 9+⊥∞+≈;≈ ;≈ +∞;⊇∞ 6†∞;≤+∞≈⊥∞≈ ∞;≈≈∞†=∞≈:

15≠ = 30 + 9 ∙ 10

&††;=&⊥†; 15≠ = 30 + 90

&††;=&⊥†; 15≠ = +120 | : 15

&††;=&⊥†; ≠ = 8


15≠ = - 200 + 32 ∙ 10

&††;=&⊥†; 15≠ = - 200 + 320

&††;=&⊥†; 15≠ = 120 | : 15

&††;=&⊥†; ≠ = 8


=&⊥†; 7+≈∞≈⊥: ≠ = 8 ∧ + = 10


4∞†⊥∋+∞ 2:


  1. 9 - ≠ = 3+

2x + 2y = 2


=> erste Gleichung umstellen:

- x = 3y - 9 —> x = -3y + 9


=> erste Gleichung in zweite einsetzen:

2 ∙ (-3y + 9) + 2y = 2

<=> -6y + 18 + 2y = 2

<.....

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&††;=&⊥†; 4+ = -16 | : (-4)

&††;=&⊥†; + = 4


=&⊥†; ≠-3∞+† +∞+∞≤+≈∞≈ ⊇∞+≤+ +-3∞+† ∞;≈≈∞†=∞≈ ;≈ ∞+≈†∞ 6†∞;≤+∞≈⊥:

≠ = - 3 ∙ 4 + 9

&††;=&⊥†; ≠ = - 12 + 9

&††;=&⊥†; ≠ = -3


=&⊥†; 0+++∞:

9 - (-3) = 3 ∙ 4 2 ∙ (-3) + 2 ∙ 4 = 2

&††;=&⊥†; 9 + 3 = 12 &††;=&⊥†; - 6 + 8 = 2

&††;=&⊥†; 12 = 12 &††;=&⊥†; 2 = 2

=&⊥†; 7+≈∞≈⊥: ≠ = -3 ∧ + = 4


+) 1/3≠ + 2/7+ = 6

3+ - 7≠ = 0


=&⊥†; ∞+≈†∞ 6†∞;≤+∞≈⊥ ∋;† 3 ∋∞††;⊥†;=;∞+∞≈:

1/3≠ + 2/7+ = 6 | ∙ 3

&††;=&⊥†; ≠ + 6/7+ = 18


=&⊥†; 6†∞;≤+∞≈⊥ ∞∋≈†∞††∞≈ ∞≈⊇ ∋≈≈≤+†;∞ß∞≈⊇ ;≈ ⊇;∞ =≠∞;†∞ ∞;≈≈∞†=∞≈:

≠ = 18 - 6/7


3+ - 7 ∙ (18 - 6/7) = 0

&††;.....

&††;=&⊥†; 9+ - 126 = 0 | +126

&††;=&⊥†; 9+ = 126 | :9

&††;=&⊥†; + = 14


=&⊥†; ≠-3∞+† +∞+∞≤+≈∞≈ ⊇∞+≤+ ∞;≈≈∞†=∞≈ ⊇∞≈ +-3∞+†∞≈:

≠ = 18 - 6/7 ∙ 14

&††;=&⊥†; ≠ = 18 - 12

&††;=&⊥†; ≠ = 6


=&⊥†; 0+++∞:

1/3 ∙ 6 + 2/7 ∙ 14 = 6 3 ∙ 14 - 7 ∙ 6 = 0

&††;=&⊥†; 2 + 4 = 6 &††;=&⊥†; 42 - 42 = 0

&††;=&⊥†; 6 = 6 &††;=&⊥†; 0 = 0


=&⊥†; 7+≈∞≈⊥: ≠ = 6 ∧ + = 14


4∞†⊥∋+∞ 3:

  1. 15≠ - 17+ = 11

25≠ + 4+ = 83


=&⊥†; ≠ ≈+†† +∞†+∋⊥≈⊥†∞;≤+∞ 9+∞††;=;∞≈†∞≈ ∞++∋††∞≈:


=> 15x -17y = 11 | ∙ 5

<=> 75x - 85y = 55


=> 25x + 4y = 83 | ∙ 3

<=> 75x + 12y = 249


=> Subtraktionsverfahren:

75x + 85y = 55

(—) 75x + 12y = 249

—.....

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-97+ = -194 | :(-97)

+ = 2


=&⊥†; 9;≈≈∞†=∞≈ ;≈ +∞;⊇∞ 6†∞;≤+∞≈⊥∞≈:

15≠ - 17 ∙ 2 = 11

&††;=&⊥†; 15≠ - 34 = 11 |&≈+≈⊥;+ 34

&††;=&⊥†; 15≠ = 45 | :15

&††;=&⊥†; ≠ = 3


25≠ + 4 ∙ 2 = 83

&††;=&⊥†; 25≠ + 8 = 83 | - 8

&††;=&⊥†; 25≠ = 75 |&≈+≈⊥;: 25

&††;=&⊥†; ≠ = 3


=&⊥†; 7+≈∞≈⊥: ≠ = 3 ∧ + = 2


+) 1/7≠ - 3/4+ = 16

- 3/14≠ + 1/5+ = -5,5


=&⊥†; 3++≤+∞ +∞≈∞;†;⊥∞≈:


1/7≠ - 3/4+ = 16 | ∙ 28

&††;=&⊥†; 4≠ - 21+ = 446


-3/14≠ + 1/5+ = -5,5 |&≈+≈⊥;∙ 70

&††;=&⊥†; -15≠ + 14+ = - 385


=&⊥†; + ≈+†† +∞†+∋⊥≈⊥†∞;≤+∞ 9+∞††;=;∞≈†∞≈ ∞++∋††∞≈:


=&⊥†; 4≠ - 21+ = 446 | ∙ 2

&.....


=&⊥†; -15≠ + 14+ = -385 | ∙ 3

&††;=&⊥†; -45≠ + 42+ = -1155


=&⊥†; 4⊇⊇;†;+≈≈=∞+†∋++∞≈:


8≠ - 42+ = 896

(+) -45≠ + 42+ = - 1155

————————————-

- 37≠ = - 259 |&≈+≈⊥;: (-37)

≠ = 7


=&⊥†; 9;≈≈∞†=∞≈ ;≈ +∞;⊇∞ 6†∞;≤+∞≈⊥∞≈:

4 ∙ 7 - 21+ = 448 - 15 ∙ 7 + 14+ = -385

&††;=&⊥†; 28 - 21+ = 448 | - 28 &††;=&⊥†; - 105 + 14+ = -385 | +105

&††;=&⊥†; - 21+ = 420 |&≈+≈⊥;: (-21) &††;=&⊥†; 14+ = -280 |&≈+≈⊥;:14

&††;=&⊥†; + = - 20 &††;=&⊥†; + = - 20


=&⊥†; 7+≈∞≈⊥: ≠ = 7 ∧ + = -20


Aufgabe 4:


a) x + y = 38

x ∙ 4 - 12 = y ∙ 3


=> erste Gleichung mit 4 multiplizieren und zweite Gleichung umstellen:


x + y = 38 | ∙ 4

.....

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=&⊥†; ≠ ∙ 4 - 12 = + ∙ 3 —&⊥†; 4≠ - 3+ = 12


=&⊥†; 3∞+†+∋∂†;+≈≈=∞+†∋++∞≈:

4≠ + 4+ = 152

(—) 4≠ - 3+ = 12

——————————

7+ = 140 | :7

+ = 20


=&⊥†; 1≈ +∞;⊇∞ 6†∞;≤+∞≈⊥∞≈ ∞;≈≈∞†=∞≈:

4≠ + 4 ∙ 20 = 152

&††;=&⊥†; 4≠ + 80 = 152 |&≈+≈⊥;- 80

&††;=&⊥†; 4≠ = 72 |&≈+≈⊥;:4

&††;=&⊥†; ≠ = 18


4≠ - 3 ∙ 20 = 12

&††;=&⊥†; 4≠ - 60 = 12 | + 60

&††;=&⊥†; 4≠ = 72 | :4

&††;=&⊥†; ≠ = 18


=&⊥†; 7+≈∞≈⊥: ≠ = 18 ∧ + = 20 . 8;∞ 8;††∞+∞≈= ⊇∞+ +∞;⊇∞≈ 5∋+†∞≈ +∞†+=⊥† 2.


+) ≠ = 4††∞+ ⊇∞≈ 2∋†∞+≈ , + = 4††∞+ ⊇∞≈ 3++≈∞≈


≠ - 1 = 3(+-1)

≠ - 9 = 5(+-9)


=&⊥†; ≠ - 1 = 3+ -3

≠ - 9 = 5+ - 45


=&⊥†; 6†∞;≤+∞≈⊥∞≈ ∞∋≈†∞††∞≈ ∞≈⊇ 3∞+†+∋.....

≠ - 3+ = -2

(—) ≠ - 5+ = -36

————————-

2+ = 34 | :2

+ = 17


=&⊥†; 9;≈≈∞†=∞≈ ;≈ +∞;⊇∞ 6†∞;≤+∞≈⊥∞≈:

≠ - 3 ∙ 17 = -2

&††;=&⊥†; ≠ - 51 = -2 | +51

&††;=&⊥†; ≠ = 49


≠ - 5 ∙ 17 = -36

&††;=&⊥†; ≠ - 85 = -36 | +85

&††;=&⊥†; ≠ = 49


=&⊥†; 7+≈∞≈⊥: ≠ = 49 ∧ + = 17. 8∞+ 2∋†∞+ ;≈† 49 ∞≈⊇ ⊇∞+ 3++≈ 17.


≤)

(1) ≠ + + + = = 20

(11) = = 3+

(111) ≠ = 5 + +


=&⊥†; (11) + (111) ;≈ (1) ∞;≈≈∞†=∞≈:

5 + + + + + 3+ = 20

&††;=&⊥†; 5 + 5+ = 20 | - 5

&††;=&⊥†; 5+ = 15 | :5

<=> y = 3


=> y einsetzen:

z = 3 ∙ 3 = 9

x = 5 + 3 = 8


=> 8 + 3 + 9 = 20


=> Lösung: x = 8 ∧ y = 3 ∧ z = 9 . Die Zahl .....



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