Question

Cine poate sa imi rezolve si mie 8 si 9 ?

Answer 1

8.a) 5(x+y)=4(2x+y)

5x+5y=8x+4y

5x-8x=4y-5y

-3x=-y=>3x=y

daca 3x=y=>x/y=x/3x care se simplifica cu x=1/3

b) 3(3x+4y)=7(2x+y)

9x+12y=14x+7y

9x-14x=7y-12y

-5x=-5y=>5x=5y=>x=5y/5 care se simplifica cu 5=>x=y

daca x=y=>x/y=1

c) 2(6x+4y)=3(5x+2y)

12x+8y=15x+6y

12x-15x=6y-8y

-3x=-2y=>3x=2y=>x=2y/3

daca x=2y/3=>x/y=2y/3/y=2y/3:y=2y/3 ori 1/y=2y/3y care se simplifica cu y=2/3

d) 3(5x-4y)=7(2x-y)

15x-12y=14x-7y

15x-14x=-7y+12y

x=5y

daca x=5y=>x/y= 5y/y care se simplifica cu y=5

9 a) x/3=y/4=> 4x=3y=>x=3y/4

3x+4y=75

3 ori 3y/4+4y=75

12y/4+4y=75 (aduc la acelasi numitor)

12y/4+16y/4=75

28y/4=75=>y= 75 ori 4/28=>y=300/28 care se simplifica cu 4=75/7

daca y=75/7 si x=3y/4=>x=3 ori 75/7/4=225/7/4=225/7 ori 1/4=225/28

deci x=75/7 si y=225/28

b) x/5=y/7=>7x=5y=>x=5y/7

x+y=24

5y/7+y=24 (aduc la acelasi numitor)

5y/7+7y/7=24

12y/7=24=>y= 24 ori 7/12=>y=14

daca y=14 si x=5y/7=>x=5 ori 14/7=>x=10

deci x=10 si y=14

c)x/4=y/5=z/6

si x+y+z=15

x/4=y/5=z/6=k

x/4=k=>x=4k

y/5=k=>y=5k

z/6=k=>z=6k

x+y+z=15

4k+5k+6k=15

15k=15=>k=15/15=>k=1

daca x=4k si k=1=>x=4

y=5k si k=1=>y=5

z=6k si k=1=>z=6