Question

6. Rezolvaţi prin metoda reducerii sistemele:
3x + 2 y =1 5x+4y=-4
a)
b)
(2x+3y=-2
4x + 3y = 3
C)
(3x + 5y = 8 (3x+4y=-1
S2x+y=-2 (2x- y=1
3x - 5y = 18
f)
4x + 5y = 8 (3x +2y=19
(6x+4y=-6
Sx+y=-1
d)
5x+2y=7
(2x+3y=14
h)
(4x - 5y=6
e)
​

Answer 1

Răspuns:

a) {3x + 2y= 1 | × (-2)

{5x + 4y = -4

{-6x - 4y= -2

{ 5x + 4y= -4

~~~~~~~~~~~~~~~(+)~~~~~~

-x / = -6 | × (-1)

=> x= 6

inlocuim : 5x + 4y= -4

5×6 + 4y = -4

30 + 4y = -4

4y = -4 - 30

4y = -34

y= -34 : 4 = - 34/ 4 = - 17/ 2

y= - 17

2

b) 2x + 3y = -2 | × (-1)

4x + 3y = 3

-2x - 3y = 2

4x + 3y = 3

2x / = 5

x = 5

2

inlocuim : 4x + 3y = 3

4×5 + 3y = 3

2

10 + 3y = 3

3y = 3-10

3y = -7

y = - 7

3