Question

rozwiąż metodą przeciwnych współczynników

a)

5x+3y-0

-x-2y=7

b)

3u+2v=2

5u+4v=6

c)

3s+5t=-6

1.5s-2t=-3

DAJE NAJJJJJJ :D

Answer 1

a)

 

5x+3y=0/*2

-x-2y=7/*3

 

10x+6y=0

-3x-6y=21

 

7x=21/:7

x= 3

 

15+3y=0/-15

x=3

 

3y=-15/:3

x=3

 

y=-5

x=3

 

b)

 

3u+2v=2/*-2

5u+4v=6

 

-6u-4v=-4

5u+4v=6

 

u=2

 

10+4v=6/-10

u=2

 

4v=-4/:4

u=2

 

v=-1

u=2

 

c)

 

3s+5t=-6

1.5s-2t=-3/*-2

 

3s+5t=-6

-3s+4t=6

 

9t=0

 

Niewykonalne ;D

 

Przy 9t=0 równa się ma być przekreślone.

* to jest mnożenie ;P

 

 

Answer 2

 

a)

5x + 3y = 0

-x - 2y = 7 /·5

 

5x + 3y = 0

-5x - 10y = 35

 

5x + (-5x) + 3y + (-10y) = 0 + 35

3y - 10y = 35

-7y = 35 /:(-7)

y = -5

 

5x + 3 · (-5) = 0

-x - 2 · (-5) = 35

 

5x + (-15) = 0

-x - (-10) = 35

 

5x - 15 = 0

-x + 10 = 35

 

5x = 15 /:5

-x = 35 - 10

 

x = 3

y = -5

 

 

b)

3u + 2v = 2 / · (-2)

5u + 4v = 6

 

-6u + (-4v) = -4

5u + 4v = 6

 

-6u + 5u + 4v + (-4v) = -4 + 6

-u = 2 /·(-1)

u = -2

 

3 · (-2) + 2v = 2

5 · (-2) + 4v = 6

 

-6 + 2v = 2

-10 + 4v = 6

 

2v = 2 - 6 /:2

4v = 6 - 10

 

v = 2

u = -2

 

c)

3s + 5t = -6

1,5s - 2t = -3 /·(-2)

 

3s + 5t = -6

-3s - (-4t) = 6

 

3s + (-3s) + 5t + (-4t) = 6

t = 6

 

3s + 5 · 6 = -6

1,5s - 2 · 6 = -3

 

3s + 30 = -6

1,5s - 12 = -3

 

3s = -36 /: 3

1,5s - 12 = -3

 

s = 12

t = 6