Question

Rozwiąż układ równań:

1) { 6a+9b=126
2(6+a+9+b)=54

2) {1/2x-3/4y=0
2/3x+1 1/4y=9

3) { 3x+4y=1 2/3
6x+3y= 1 1/4

Answer 1

Rozwiąż układ równań:

1) { 6a+9b=126
2(6+a+9+b)=54

{ 6a+9b=126 /:6
12+2a+18+2b=54

{ a+1,5b=21 /*(-1)
2a+2b=24 /:2

{ -a-1,5b=-21
a+b=12
---------------
-1/2b=-9
b=18
a=-6

2) {1/2x-3/4y=0 /*4
2/3x+1 1/4y=9 /*12

{2x-3y=0 /*5
8x+15y=108

{10x-15y=0
8x+15y=108
--------------
18x=108
x=6
y=4

3) { 3x+4y=5/3 *(-3)
6x+3y= 5/4 /*4

-9x-12y=-5
24x+12y=5
-----------------
15x=0
x=0
y=5/12

Answer 2

1) { 6a+9b=126
2(6+a+9+b)=54

6a + 9b = 126
12 + 2a + 18 + 2b = 54

6a + 9b = 126
2a + 2b = 54 - 12 - 18

6a + 9b = 126
2a + 2b = 24

2a = 24 - 2b |:2
a = 12 - b

6(12 - b) + 9b = 126
72 - 6b + 9b = 126
-6b + 9b = 126 - 72
3b = 54 |:3
b = 18

a = 12 - b
a = 12 - 18
a = -6


2) {1/2x-3/4y=0
2/3x+1 1/4y=9

½x - ¾y = 0
⅔x + 1 ¼y = 9

½x - ¾y = 0 |*5
⅔x + 5/4y = 9 |*3

5/2x - 15/4y = 0
6/3x + 15/4y = 27


5/2x + 6/3x = 27
15/6x + 12/6x = 27
27/6x = 27 |*6
27x = 162 |:27
x = 6

1/2x - 3/4y = 0
3 - 3/4y = 0
-3/4y = -3 |*(-4)
3y = 12 |:3
y = 4


3) { 3x+4y=1 2/3 |*2
6x+3y= 1 1/4

6x + 8y = 5/3 * 2
6x + 3y = 1 ¼

6x + 8y = 10/3
6x + 3y = 1¼

6x = 10/3 - 8y

podstawiamy:
10/3 - 8y + 3y = 1¼
-8y + 3y = 1¼ - 10/3
-5y = 5/4 - 10/3
-5y = 15/12 - 50/12
-5y = -35/12 |:(-5)
y = 35/12 * ⅕
y = 35/60
y = 7/12

6x = 10/3 - 8y
6x = 10/3 - 8*7/12
6x = 10/3 - 56/12
6x = 40/12 - 56/12
6x = -16/12
6x = - 4/3 |:6
x = -4/3 * ⅙
x = -4/18
x = -2/9