Question

Rozwiąz uklad równań metoda algebraiczną:
a) 7x-3y =15
5x+6y=27
b) 7x-3y+1=0
4x-5y+17=0
c) 3x+5y=4
7x-3y=2
d) x-7y=3
5x-21y=11
e) -8x+3y=15
7x-2y=0
f) 2x+y=4
x-2y=7
bardzo prosze o pomoc

Answer 1

Metoda algebraiczna ma 3 wersje:
1. metoda podstawiania
2. metoda przeciwnych wqspółczynników
3. metoda wyznaczników

zadania poniższe są rozwiazane metodą drugą i pierwszą

a) metoda prezeciwnych współczynników
7x-3y =15 /*2
5x+6y=27

14x -6y = 30 | +
5x + 6y = 27 |
-----------------------
19x = 57
x = 57:19
x = 3
5*3 + 6y = 27
6y = 27 -15
6y = 12
y = 12 : 6
y = 2
x = 3
y = 2

b)
7x-3y+1=0
4x-5y+17=0


7x -3y = -1 /*5
4x -5y = -17 /*(-3)

35x - 15y = -5 |
-12x + 15y = 51 | +
----------------------
23x = 46
x = 46 : 23
x = 2

4*2 -5y = -17
-5y = -17 -8
y = (-25): (-5)
y = 5

x = 2
y = 5

c) metoda podstawiania
3x+5y=4
7x-3y=2


3x = 4 -5y
7x -3y = 2

x = 1/3(4 -5y)
7*1/3(4 -5y) -3y = 2

x = 1/3(4 -5y)
28/3 - (35/3)y -3y = 2

x = 1/3(4 -5y)
( -35/3)y - (9/3)y = 6/3 - 28/3

x = 1/3(4 -5y)
(- 44/3)y = (- 22/3)

x = 1/3(4 -5y)
y = (-22/3):(-44/3)

x = 1/3(4 -5y)
y = (-22/3)*(-3/44)

x = 1/3(4 -5y)
y = 1/2

x = 1/3( 4 - 5*1/2) = 1/3( 8/2-5/2)= 1/3*(3/2)= 1/2
y = 1/2

x = 1/2
y = 1/2

d)
x-7y=3
5x-21y=11

x = 3 + 7y
5*(3 + 7y) - 21y = 11

x = 3 + 7y
15 + 35y -21y = 11

x = 3 + 7y
14y = 11-15

x = 3 + 7y
y = (-4) : 14

x = 3 + 7y
y = - 2/7

x = 3 + 7*(-2/7)= 3 - 2 = 1
y = -2/7

x = 1
y = -2/7

e)
-8x+3y=15
7x-2y=0

-8x + 3y = 15
-2y = -7x

-8x + 3y = 15
y = -7x : (-2)

-8x + 3y = 15
y = (7/2)x

-8x + 3(7/2x) = 15
y = 7/2x

- 16/2x + 21/2x = 15
y = 7/2x

5/2x = 15
y = 7/2x

x = 15 : (5/2)
y = 7/2 x

x = 15*(2/5)
y = 7/2x

x = 6
y = 7/2*6 = 21

x = 6
y = 21

f)
2x+y=4
x-2y=7

y = 4 -2x
x -2(4 -2x) = 7

y = 4 -2x
x - 8 + 4x = 7

y = 4 -2x
5x = 7 +8

y = 4 -2x
x = 15 : 5 = 3

y = 4 -2*3 = 4 -6 = -2
x = 3

x = 3
y = -2