za ucenike 9 razreda

1. LINEARNE JEDNAČINE SA
DVIJE NEPOZNATE
Nastavnik: Brankica Jokić

2. 2
LINEARNA JEDNAČINA SA DVIJE NEPOZNATE- ponovimo!
ax+by+c=0 ili y=kx+n linearna jednačina sa dvije nepoznate.
Ako je ax1 + by1=c tačna brojevna jednakost, onda je par realnih brojeva
(x1, y1) rješenje linenarne jednačine ax+by=c.
Sva rješenja jednačine ax+by=c određuju skup rješenja te jednačine.
Riješiti jednačinu ax+by=c znači odrediti skup njenih rješenja.
Skup rješenja linearne jednačine ax+by=c predstavlja sve tačke prave,
grafika odgovarajuće linearne funkcije.
Za jednačinu ax+by=c kažemo da je najjednostavniji ili sređeni
oblik linearne jednačine sa dvije nepoznate.

3. 3
SISTEM LINEARNIH JEDNAČINA SA DVIJE NEPOZNATE
Posmatrajmo dvije jednačine 3x-y=-6 i x+2y=5
Provjerimo da li su parovi brojeva rješenja datih jednačina (-3,4), (1,9) i (-1,3)
Zaključujemo! Zajedničko rješenje jednačina je (-1,3)

4. 4
Napomenimo samo da dati sistem može imati: jedinstveno rešenje, beskonačno
mnogo rješenja (neodređen) ili pak da nema rješenja (nemoguć).
1. Ako par brojeva (x0,y0) koji predstavlja zajedničko rješenje linearnih jednačina
ax1 + by1=c i ax2 + by2=c2, naziva se rješenje sistema ovih dviju linearnih jednačina.
Sistem dvije linearne jednačine sa dvije nepoznate je određen ako ima tačno jedno
rješenje.

5. 5
2. Ako su koeficijenti pravca dvije linearne jednačine sa dvije nepoznate y=k1x+n1 i
y=k2x+n2 jednaki, k1=k2 i n1 ≠ n2 system je nemoguć odnosno nema rješenja.

6. 6
3. Ako grafički prikaz sistema dvije linearne jednačine sa dvije nepoznate
čine dvije prave koje se poklapaju , tada taj system ima beskonačno
mnogo rješenja k1=k2 i n1=n2

7. Učiteljica Ivici: Ivice koliko je 8+8?
Ivica: Ne znam!
Učiteljica: Pogledaj - ako u jednoj ruci imam 8
jabuka, a u drugoj isto 8 što onda imam?
Ivica: Velike ruke učiteljice!!
ZADAĆA:
MATEMATIKA 9, strana 107, zadatak 7.5
😉

8. This is a slide title
✘ Here you have a list of items
✘ And some text
✘ But remember not to overload your slides
with content
Your audience will listen to you or read the
content, but won’t do both.
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9. Big concept
Bring the attention of your audience over a
key concept using icons or illustrations
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10. White
Is the color of milk and
fresh snow, the color
produced by the
combination of all the
colors of the visible
spectrum.
You can also split your content
Black
Is the color of coal, ebony,
and of outer space. It is the
darkest color, the result of
the absence of or complete
absorption of light.
10

11. In two or three columns
Yellow
Is the color of gold,
butter and ripe
lemons. In the
spectrum of visible
light, yellow is found
between green and
orange.
Blue
Is the colour of the
clear sky and the
deep sea. It is located
between violet and
green on the optical
spectrum.
Red
Is the color of blood,
and because of this it
has historically been
associated with
sacrifice, danger and
courage.
11

12. A picture is worth a thousand words
A complex idea can be conveyed with just a single still image, namely
making it possible to absorb large amounts of data quickly.
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13. Use charts to explain your ideas
GrayWhite Black
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14. And tables to compare data
A B C
Yellow 10 20 7
Blue 30 15 10
Orange 5 24 16
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15. Maps
our office
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18. Our process is easy
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18

19. Let’s review some concepts
Yellow
Is the color of gold, butter and
ripe lemons. In the spectrum of
visible light, yellow is found
between green and orange.
Blue
Is the colour of the clear sky and
the deep sea. It is located
between violet and green on the
optical spectrum.
Red
Is the color of blood, and because
of this it has historically been
associated with sacrifice, danger
and courage.
Yellow
Is the color of gold, butter and
ripe lemons. In the spectrum of
visible light, yellow is found
between green and orange.
Blue
Is the colour of the clear sky and
the deep sea. It is located
between violet and green on the
optical spectrum.
Red
Is the color of blood, and because
of this it has historically been
associated with sacrifice, danger
and courage.
19

20. You can copy&paste graphs from Google Sheets
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or software projects using these
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25. THANKS!
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You can find me at
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✘ user@mail.me
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26. Credits
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✘ Photographs by Unsplash
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28. 28
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