9SISTEMA DE EQUAÇÃO DO PRIMEIRO GRAU

iguale a incógnita y multiplicando a segunda equação por 2

x 2y = 112x − 2y = 10→

x 2y = 11 2x − 2y = 10

3x 0 = 21

→

3x = 21

x = 213

x = 7

→x 2y = 11x − y = 5 . 2

01

iguale a incógnita y tirando o m.m.c. de 2 e 3multiplica-se a primeira equação por 2 e a segunda por 3

→4x 6y = 16

15x − 6y = 319x 0 = 19

→

19x = 19

x = 1919

x = 1

→2x 3y = 8 . 25x − 2y = 1 . 3

4x 6y = 1615x − 6y = 3

7 2y = 112y = 11 − 72y = 4y = 2

4 . 1 6y = 166y = 16 − 46y = 12y = 2

→

→

02

x y = 32 x − y = 10

2x 0 = 42

2x = 42x = 21

21 y = 32y = 32 − 21y = 11

03

04 x 2y = 27x − y = −3 . 2

x 2y = 272x − 2y = −6

x 2y = 27 2x − 2y = −6

3x 0 = 213x = 21x = 7

7 2y = 272y = 27 − 72y = 20y = 10

05 x 2y = 33x y = 4 . −2

x 2y = 3 −6x − 2y = −8

−5x 0 = −5

5x = 5x = 1

1 2y = 32y = 3 − 12y = 2y = 1

2x 2y = 123x − 2y = 13

Método: ADIÇÃO

08 3x − y = 1 . 2x 2y = 5

6x − 2y = 2 x 2y = 5

7x 0 = 77x = 7x = 1

1 2y = 52y = 5 − 12y = 4y = 2

6x − 2y = 2x 2y = 5

09 x y = 6 . 23x − 2y = 13

2x 2y = 12 3x − 2y = 13

5x 0 = 255x = 25x = 5

2 . 5 2y = 122y = 12 − 102y = 2y = 1

2x 2y = 123x − 2y = 13

0606 x 3y =−42x − y = 6 . 3

x 3y =−46x − 3y = 18

x 3y = −4 6x − 3y = 18

7x 0 = 147x = 14x = 2

2 3y = −43y =−4 − 723y =−6y = −2

07 2x 5y = 17 . 23x − 2y = 16 . 5

4x 10y = 3415x − 10y = 80

4x 10y = 34 15x − 10y = 80

19x 0 = 14419x = 144x = 6

4 . 6 10y = 3410y = 34 − 2410y = 10y = 1

10 2x 3y = 74x y = 9 . −3

2x 3y = 7 −12x − 3y =−27

−10x 0 =−20

10x = 20x = 2

2 . 2 3y = 73y = 7 − 43y = 3y = 1

2x 3y = 7−12x − 3y =−27

11 x y = 5 x − y = 1

2x 0 = 6

2x = 6x = 3

3 y = 5y = 5 − 3y = 2

12x 2y = 7

x − 2y = 32x 0 = 10

2x = 10x = 5

5 2y = 72y = 7 − 52y = 2y = 1

Método: SUBSTITUIÇÃO

x = 1 − 2y2x − y = 7

2 1 − 2y − y = 72 − 4y − y = 7−5y = 5y = −1

x = 1 − 2 . −1x = 1 2x = 3

13

x = 10 − yx − y = 2

10 − y − y = 2−2y =−8y = 4

x = 10 − 4x = 614

x = 11 − yx − y = 1

11 − y − y = 1−2y =−10y = 5

x = 11 − 5x = 615

x = 46 − yx − y = 14

46 − y − y = 14−2y =−32y = 16

x = 46 − 16x = 3016

x = 3 − yx − y = 1

3 − y − y = 1−2y =−2y = 1

x = 3 − 1x = 217

2x 2x = 124x = 12x = 3

y = 2 . 3x = 618

2x y = 12y = 2x

7 − 2y − 2y = 3−4y =−4y = 1

x = 7 − 2 . 1x = 5

19 x = 7 − 2yx − 2y = 3

2 −1 y − y = 4−2 2y − y = 4y = 2

x = −1 2x = 1

20 2x y = 4x = −1 y

2x − 3 11 − 2x = −12x − 33 6x =−18x = 32x = 4

y = 11 − 2 . 4y = 3

21 y = 11 − 2x2x − 3y =−1

22 3x = 13 7y ⇒ x = 13 7y3

4x 5y = 3

4 13 7y3 5y = 3

52 28y3

5y = 3

52 28y 15y = 943y = −43y = −1

x =13 7 . −1

3

x =13 − 7

3x = 2

23 2x = 17 − 5y ⇒ x = 17 − 5y2

3x − 2y = 16

3 17 − 5y2 − 2y = 16

51 15y2

− 2y = 16

51 − 15y − 4y = 32−19y = −19y = 1

3x − 2 . 1 = 163x = 18x = 6

24 5x = 19 4y ⇒ x = 19 4y5

4x 3y = 40

4 19 4y5 3y = 40

76 16y5

3y = 40

76 16y 15y = 20031y = 124y = 4

4x 3 . 4 = 404x = 28x = 7

Método: COMPARAÇÃO

25 y = 5−y = 1

y − 5 = 0−y − 1 = 0

y − 5 = −y − 1y y =−1 52y = 4y = 2

x y = 5x 2 = 5x = 5 − 2x = 3

26 y = 15−y = 1

y − 15 = 0−y − 1 = 0

y − 15 = −y − 1y y =−1 152y = 14y = 7

x y = 15x 7 = 15x = 15 − 7x = 8

27 y = 13−2y = 16

y − 13 = 0−2y − 16 = 0

y − 13 = −2y − 16y 2y = −16 133y =−3y = −1

x − y = 8x − −1 = 8x = 8 − 1x = 7

28 2y = 9−2y = 1

2y − 9 = 0−2y − 1 = 0

2y − 9 = −2y − 12y 2y = −1 94y = 8y = 2

x 2y = 9x 2 . 2 = 9x = 9 − 4x = 5

29 4y = 2−y = 7

4y − 2 = 0−y − 7 = 0

4y − 2 =−y − 74y y =−7 25y =−5y = −1

x 2y = 1x 2 . −1 = 1x = 1 2x = 3

30 3x − 3y 5y − 5x = 182x 3y = 37

−2x 2y = 182x 3y = 37

−2x 2y = 18 . −12x 3y = 37

2x − 2y = −182x 3y = 37

−2y =−183y = 37

−2y 18 = 03y − 37 = 0

−2y 18 = 3y − 37−2y − 3y = −37 − 185y = 55y = 11

2x 3y = 372x 3 . 11 = 372x = 37 − 332x = 4x = 2

31 x3− y

2= 2

x2

− y3= 3

2x − 3y = 12 . 33x − 2y = 18 . 2

6x − 9y = 366x − 4y = 36

−9y = 36−4y = 36

−9y − 36 = 0−4y − 36 = 0

−9y − 36 =−4y − 36−9y 4y = −36 36−5y = 0

y = −05

y = 0

322x 3y = 23 . 55x − 3y = 5 . 2

10x 15y = 11510x − 6y = 10

15y = 115−6y = 10

15y − 115 = 0−6y − 10 = 0

15y − 115 =−6y − 1015y 6y = −10 11521y = 105y = 5

2x − 3y = 123x − 2y = 18

3x − 2y = 183x − 2 . 0 = 183x = 18 0x = 6

10x 15y = 11510x 15 . 5 = 11510x 75 = 11510x = 115 − 7510x = 40x = 4

333x 3y = 213x − y = 5

3y = 21−y = 5

3y − 21 = 0−y − 5 = 0

3y − 21 = −y − 53y y = −5 214y = 16y = 43x − y = 5

3x − 4 = 53x = 5 43x = 9x = 3

342x 3y = 5 . 77x − 3y = 4 . 2

14x 21y = 3514x − 6y = 8

21y = 35−6y = 8

21y − 35 = 0−6y − 8 = 0

21y − 35 = −6y − 821y 6y =−8 3527y = 27y = 1

14x − 6y = 814x − 6 . 1 = 814x = 8 614x = 14x = 1

352x 4y = 16 . 55x − y = 7 . 2

10x 20y = 8010x − 2y = 14

20y = 80−2y = 14

20y − 80 = −2y − 1420y 2y = −14 8022y = 66y = 3

10x − 2y = 1410x − 2 . 3 = 1410x = 14 610x = 20x = 2

20y − 80 = 0−2y − 14 = 0

362x 2y = 3y 63x − 3y = 2x − 2

−y − 6 = −6y 4−y 6y = 4 65y = 10y = 2

2x 2y − 3y = 63x − 3y − 2x = −2

2x − y = 6x − 3y =−2

2x − y = 62x − 6y =−4

−y = 6−6y = −4

−y − 6 = 0−6y 4 = 0

x − 3y =−2x − 3 . 2 = −2x = −2 6x = 4