1. Rezolvati prin metoda substitutiei sistemelor :
a) -2x+y=2 ; 2x+y=b
b) x+ay=13 ; 4x+5y=25
c) 4x-3y=18 ; 5x-2y=19
d) 5x-4y=-38 ; 3x+2y=1
e) 6x-7y=18 ; 2x+5y=6
f) x-2y=8 ; 4x+5y=6
g) 2x+5y=-11 ; -6x+y=-47
h) 2x+4y=6 ; x-y=9


2. Rezolvati prin metoda substitutiei sistemelor :
a) 3 supra 5x+1 supra 2y =2 ; -7x+4y=-43
b) √2x-3y=-7 ; x+4y=√2+12
c) x+√7y =12 ; -3x+2√7y =-1

1

Răspunsuri

  • Utilizator Brainly
2014-04-20T17:21:56+03:00
1.a)
-2x+y=2  (1) inmultesti cu -5
3x+5y=10  (2)


10x-5y=-10  (1) 
3x+5y=10  (2)
13x=0
x=0 (3)

inlocuiesti relatia (3) in (1) =>>

0+y=2 =>>
y=2;
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c)
4x-3y=18 (1)
 5x-2y=19 (2)

inmultim relatia (1) cu -2 si relatia (2) cu 3

-8x+6y=-36 (3)
15x-6y=57
 (4)--------------(+)
7x=21
x=21/7
x=3 (5)

inlocuim relatia (5) in relatia (1)
12-3y=18
-3y=18-12
-3y=6
y=6/(-3)
y=-2

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 d)
5x-4y=-38 (1)
3x+2y=1  (2)

inmultim relatia (2) cu 2
5x-4y=-38 (1) 
6x+4y=2  (3)
------------------------(+)
11x=-36
x=-36/11 (4)

inlocuim relatia (4) in relatia (2)
3*(-36)/11 + 2y=1
-108/11 + 2y=1
aducem la acelasi numitor inmultind cu 11
-108 + 22y=11
22y=11+108
y=119/22
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e)
6x-7y=18 (1)
2x+5y=6 (2) inmultim relatia 2 cu -3

6x-7y=18       (1) 
-6x-15y=-18   (3)
------------------------------(+)
adunam (1) cu (3)
0-22y=0
y=0  (4)
inlocuim (4) in relatia (1)
y=0  (4)
6x-7y=18 (1)

6x=18
x=18/6
x=3
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f)
x-2y=8      (1) inmultesti prima relatie cu -4
 4x+5y=6   (2)


-4x+8y=-32 (3)
4x+5y=6 (2)
-------------------(+)
0+13y=-26
y=-26/13
y=-2  (4)
inlocuiesti relatia 4 in relatia 1
y=-2  (4)
x-2y=8 (1)
x+4=8
x=4
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h)
2x+4y=6 (1)
x-y=9     (2) inmultim relatia 2 cu 4


2x+4y=6 (1) 
4x-4y=36 (3)
-------------------------(+)
6x+0=30
x=30/6
x=5 (4)

inlocuim relatia 4 in relatia 2
x=5 (4)
x-y=9     (2)
5-y=9
-y=4 inmultim cu -1
y=-4

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