Question

Rozwiąż układ równań metodą podstawiania.
a. {2x-3(x+y)=14=y-2
2(x-y)+3y+3=2y-1

b. {x-y/2-1=-⅙-x-2y/3
x/3-y/2=⅚

c. {4(2a-b)/3+b/2 = 1/2(a-b)+8+2(a+b)/3
-1+3-b/4 = a+1/3

z gory dzięki ;)

Answer 1

A.
{2x-3(x+y)=14=y-2
2(x-y)+3y+3=2y-1

2x -3x-3y-14 = y-2
2x-2y +3y +3 = 2y-1

-x -3y -y = -2 +14
2x - y -2y = -1 - 3

-x - 4y = 12 /*(-1)
2x -3y = - 4

x - 4y = - 12
2x -3y = - 4

Z pierwszego równania wyznaczam x= -12 +4y
i wstawiam do drugiego równania
x= -12 +4y
2(-12 +4y) -3y = - 4

x= -12 +4y
-24 +8y -3y = - 4

x= -12 +4y
5y = -4 +24 /:5

x= -12 +4y
y = 20:5

x= -12 +4y
y = 4

x = -12 + 4*4
y = 4

x = -12 +16
y = 4

x = 4
y = 4

b. {x-y/2-1=-⅙-x-2y/3
x/3-y/2=⅚

x - ½y -1 = - ⅙ -x - ⅔y
⅓ x -½ y = ⅚ /*6

x - ½y + x +⅔y = - ⅙ + 1 /*6
2x - 3y = 5

6x - 3y + 6x +4y = -1 +6
2x - 3y = 5

12x + y = 5
2x - 3y = 5
Z pierwszego równania obliczam y = 5 - 12x i podstawiam do drugiego równania
y = 5 - 12x
2x - 3(5 - 12x ) = 5

y = 5 - 12x
2x -15 +36x = 5

y = 5 - 12x
36x = 5 +15 /:36

y = 5 - 12x
x = 60:36

y = 5 - 12x
x = ⅚

y = 5 - 12*⅚
x = ⅚

y = 5 - 10
x = ⅚

y = - 5
x =⅚

c.
4(2a-b)/3+b/2 = 1/2(a-b)+8+2(a+b)/3
-1+3-b/4 = a+1/3

8/3a - 4/3b + ½b = ½a - ½b + 8 + ⅔ a + ⅔b /*6
- 1 + 3 - ¼b = a + ⅓ /*12

16a - 8b + 3b = 3a - 3b +48 + 4a + 4b
-12 + 36 - 3b = 12a + 4

16a -5b = 7a +b +48
-3b -12a = 4 +12 -36

16a -5b - 7a - b = 48
-3b -12a = -20 /:(-1)

9a - 6b = 48 /:3
3b + 12a = 20

3a -2b = 16
3b + 12a = 20

-2b = 16 -3a /:(-2)
3b + 12a = 20

b = -( 3a -16): (-2)
3b + 12a = 20
Z pierwszego równania obliczam b = ( 3a -16):2 i wstawiam do drugiego równania
b = ( 3a -16):2
3*[( 3a -16):2 ] + 12a = 20

b = ( 3a -16):2
9/2a - 24 +12a = 20

b = ( 3a -16):2
4,5a +12a = 20+24

b = ( 3a -16):2
16,5 a = 44

b = ( 3a -16):2
33/2a = 44

b = ( 3a -16):2
a = 44 *2/33

b = ( 3a -16):2
a = 8/3

b = [ 3*8/3) -16 ] :2
a = 8/3

b = (8 -16):2
a = 8/3

b =(-8) :2
a = 8/3

b = - 4
a = 8/3