Question

rapiid dau coroană va rooog​

Answer 1

I

1. 5x+3y=4   [ simplificam +3 cu (-3)] si adunam 5x+4x .

  4x-3y=14

 --------------

  9x=18

    x=2

5x+3y=4

5*2+3y=4

10+3y=4

3y=6

y=2

2.

$\left \{ {{ax-y=1} \atop {2x+by=12}} \right.$

(3:2) => x=3, y=2

=> a*3-2=1

    3a=1+2

    3a=3 =>

=> a=1

2*3+b*2=12

6+2b=12

2b=12-6

2b=6

=> b=3

3. ax2+ax3+a:2+a:3=70

ax2+ax3+a:2+a=70x3=210  

ax2+ax3+2a=210x2=420  

ax2+3a=420:3=140  

4a=70  

a=17.5

4. 4x+ay=6

  -4+2a=6  

   2a=10

   a=5

5.

O sa notam "b" pentru baieti si "f" pentru fete

b+f=32

b=3f

3f+f=32

4f=32

f=8

b=3x8

b=24

=> 8 fete si 24 baieti.

6.

x+3y=0

3x+4y=-5

=>

x=-3y;

-9y+4y=-5

=>

x=-3y;

-5y=-5

=>

x=-3; y=1

II

1.

x-pretul initial

x + 25x/100= 750

100x/100 +25x/100=750

125x/100=750

125x=75000

x=600  => D.600 lei

2.

x+2y=-1

2x+y=4

=> x=-1-2y

    2x+y=4

=> 2(-1-2y)+y=4

=>  y=-2

=>  x=-1-2*(-2)

=>  x=3

=>(x,y)=(3;-2) => C. (3;-2)

3.

notam numerele a si b.

(a+b)/(a-b)=6 =>a+b=6a-6b

3a-2b=66 =>3a=66+2b =>a=(66+2b)/3

(66+2b)/3 + b = 2(66+2b) - 6b

66+2b+3b=6(66+2b)-18b

66+5b=396-6b

11b=396-66

11b=330 =>b=30 =>a=42

=> A. (42;30)

4.

$\left \{ {{\sqrt{3}x-2\sqrt{2}x =-\sqrt{6} } } \atop {2\sqrt{3}x+\sqrt{2}y =3\sqrt{6} }} \right. =>\left \{ {{\sqrt{3}x-2\sqrt{2}y =-\sqrt{6} } \atop {x=\frac{3\sqrt{2} }{2}-\frac{\sqrt{6} y}{6} }} \right. => \sqrt{3} * (\frac{3\sqrt{2} }{2} - \frac{\sqrt{6} y}{6} - 2\sqrt{2}y = - \sqrt{6} => y=\sqrt{3} => x=\frac{3\sqrt{2} }{2} -\frac{\sqrt{6}* \sqrt{3} }{6} => x=\sqrt{2} => (x;y) = (\sqrt{2};\sqrt{3} ) => C.(\sqrt{2};\sqrt{3} )$