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Rezolvati in RxR prin metoda reducerii sistemul de ecuatii:
a)[tex] \left \{ {{2x-3y=5} \atop {x+y=10}} \right. [/tex]
b)[tex] \left \{ {{x-y=-1} \atop {3x+2y=7}} \right. [/tex]
c)[tex] \left \{ {{40x+3y=15} \atop 10x-11y=9}} \right. [/tex]
d)[tex] \left \{ {{x+2y=5} \atop 3x-6y=9}} \right. [/tex]
e)[tex] \left \{ {{2x-4y=-6} \atop 3x-2y=-7}} \right. [/tex]}
f)[tex] \left \{ {{5x-2y=1} \atop 15x-3y=-3}} \right. [/tex]
g)[tex] \left \{ {12x-7y=2} \atop {15x-5y=-5}} \right. [/tex]
h)[tex] \left \{ {{2x+3y=5} \atop 5x+2y=-2}} \right. [/tex]

Răspuns :

Renatemambouko
a)
2x-3y=5
x+y=10  inmultim cu 3
3x+3y=30
se aduna 
2x-3y=5
3x+3y=30
5x=35
x=7
y=10-7=3

b)
x-y=-1  inmultim cu 2
3x+2y=7
2x-2y=-2
5x=5
x=1
y=2

c)40x+3y=15     
10x-11y=9       inmultim cu -4
40x+3y=15
-40x+44y=-36
47y=-21
y=-21/47
x=(9+11y)/10=[9+11(-21/47)]/10=(423-231)/470=192/470=96/235

d) x+y=5   inmultim cu 6
    3x-6y=9
6x+6y=30
3x-6y=9
9x=39
x=39/9
y=5-x=5-39/9=(45-39)/9=6/9=2/3

e) 2x-4y=-6 
3x-2y=-7   inmultim cu -2
-6x+4y=14
 2x-4y=-6 
-4x=8
x=-2
y=(3×(-2)+7)/2=(-6+7)/2=1/2

f) 5x-2y=1   inmultim cu -3
15x-3y=-3
-15x+6y=-3
9y=-6
y=-2/3
x=[1+2(-2/3)]/5=(1-4/3)/5= -1/15

g) 12x-7y=2     inmultim cu -5
    15x-5y=-5    inmultim cu 7
-60x+35y=-10
105x-35y=-35
45x=-45
x=-1
y=[-2+12×(-1)]/7=(-2-12)/7=-2

h) 2x+3y=5    inmultim cu -2
    5x+2y=-2   inmultim cu 3
-4x-6y=-10
15x+6y=-6
11x=-16
x=16/11
y= (5-2×16/11)/3= (55-32)/11×3=23/33

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