Question

Witam.

Uprzejmie proszę o pomoc.

Układy równań, 4 przykłady.

Zadanie w załączniku.

Z góry dziękuję

Answer 1

a)

x/12 + y/8= 1      /* 24

(x-2)/4 –(y-6) =3    /*4

 

2x + 3y =24

x-2 – 2(y-6) =12

 

2x+ 3y = 24

x-2-2y +12 =12

 

2x+3y = 24

x-2 y =2    /* (-2)

 

2x+3y= 24

-2x +4y=-4

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7y = 20  /:7

y= 20/7

y = 2 i 6/7

2x + 3* 20/7=24

2x= 24 – 60/7

2x = 24-8 i 4/7

2x= 15 i 3/7

 x=108/7 * ½= 108/14= 54/7

 

x=7 i 5/7

y = 2 i 6/7

 

b)

x/5 – y/2 = 4   /*10

(x-2)/3 + (y+2)/2 = 2   /*6

 

2x  - 5y =40

2x-4 +3y+6 = -6

 

2x-5y =40

2x + 3y = -8 /* (-1)

 

2x -5y = 40

-2x-3y = 8

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-8y =  48  /: (-8)

x= -6

2x – 5 *(-6) = 40

2x +30 =  40

2x = 40 -30

2x = 10

x = 5

 

x = 5

y= -6

 

c)

(3x-1)/2 – (4y-7)/3 = 2    /* 6

(3y-6)/4 – (5-x)/6 = - 1 i 5/12    /*12

 

3(3x-1) – 2(4y-7) = 12

3(3y -6) -2(5-x) = - 17

 

9x -3 -8y + 14 = 12

9y -18 -10 + 2x = -17

 

-8y +9x  = 1    

9y + 2x = 11 /* (-4,5)

 

-8y +9x = 1

-40,5y -9x = -49,5

----------------------- 

-48,5y = -48,5   /: (-48,5)

y= 1

-8 +9x =1

9x = 9

 

x=1

y= 1

 

d)

(2x-y)/5 –y+ 2x = 1,2  /*5

(2x+3y)/12 – (4x-y)/8 = 0,25   /*24

 

2x-y -5y + 10x =6

2(2x+3y) -3(4x-y) = 6

 

12x -6y = 6   /:6

4x +6y -12x + 3y = 6

 

  2x – y=1    

-8x + 9y = 6

 

2x – y=1     /* 9

-8x+9y = 6

 

18x -9y =9

-8x +9y = 6

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10x =15 /:10

x= 1,5

2 * 1,5 –y =1

-y = 1-3

-y =  -2 /*(-1)

 

y= 2

x= 1,5