EXERCÍCIOS DA UNIDADE II MÓDULO 7

Prévia do material em texto

�PAGE �
�PAGE �2�
EXERCÍCIOS DA UNIDADE II MÓDULO 7
I) Resolva os seguintes sistemas, aplicando o método da substituição.
1) 
 2) 
 
 x + y = 4 2x + y = 8 x = 4 – y 2x = 8 x – y = 20
 x = 4 – y 2 (4 – y) + y = 8 x = 4 – 0 x = 8 : 2 4 – y = 20
 8 – 2y + y = 8 x = 4 x = 4 – y = 20 – 4
 – 2y + y = 8 – 8 – y = 16
 – y = 0 y = – 16
 y = 0
 S = {4, 0} S = {4, – 16}
 
3) 
 4) 
 x + y = 6 x – 2y = 12 x = 6 – y x – y = – 1 2x + y = 4 x = – 1 + y 
 x = 6 – y 6 – y – 2y = 12 x = 6 – (– 2) x = – 1 + y 2(– 1 + y) + y = 4 x = – 1 + 2
 – y – 2y = 12 – 6 x = 6 + 2 – 2 + 2y + y = 4 x = 1
 – 3y = 6 x = 8 2y + y = 4 + 2
 3y = – 6 3y = 6
 y = – 6 : 3 y = 6 : 3
 y = – 2 y = 2
 S = {8, – 2} S = {1, 2}
 II) Resolva os seguintes sistemas, aplicando o método da adição.
1) 
 2) 
 
 
 
 
 
 6x + 3y = 33 2x + y = 11 6x + 8y = 58 3x + 4y = 29
 2x – 3y = – 1 2.4 + y = 11 36x – 8y = 68 3.3 + 4y = 29
 8x = 32 8 + y = 11 42x = 126 9 + 4y = 29
 x = 32 : 8 y = 11 – 8 x = 126 : 42 4y = 29 – 9 y = 20 : 4 
 x = 4 y = 3 x = 3 4y = 20 y = 5 
 
 S = {4, 3} S = {3, 5}
3) 
 4) 
 
 
 
 15x – 12y = 57 5x – 4y = 19 x + 2y = 1 x + 2y = 1
 16x + 12y = 160 5.7 – 4y = 19 4x – 2y = 14 3 + 2y = 1
 31x = 217 35 – 4y = 19 5x = 15 2y = 1 – 3
 x = 217 : 31 – 4y = 19 – 35 x = 15 : 5 2y = – 2
 x = 7 – 4y = – 16 x = 3 y = – 2 : 2
 4y = 16 y = – 1
 y = 16 : 4
 y = 4 
 S = {7, 4} S = {3, – 1}
III) Resolva os seguintes sistemas, aplicando o método da comparação.
1) 
 2) 
 2x + 3y = 14 3x – 5y = 2 7x + 2y = 15 3x + 2y = 7
 2x = 14 – 3y 3x = 2 + 5y 7x = 15 – 2y 3x = 7 – 2y
 x = 
 x = 
 x = 
 x = 
 
 = 
 
 = 
 
3(14 – 3y) = 2(2 + 5y) 19y = 38 3(15 – 2y) = 7(7 – 2y) 
42 – 9y = 4 + 10y 45 – 6y = 49 – 14y
– 9y – 10y = 4 – 42 y = 38 : 19 – 6y + 14y = 49 – 45
– 19 y = – 38 y = 2 8y = 4 y = 
 y = 
x = 
 x = 
 x = 
 x = 
 x = 2
x = 
 x = 4 x = 
 x = 
x = 
 S = {4, 2} S = { 1/2, 2}
3) 
 4) 
 
 
x – y = 13 x + y = 17 2x = 3y + 1 2x = 31 – 7y 
x = 13 + y x = 17 – y x = 
 x = 
 
 13 + y = 17 – y 
 = 
y + y = 17 – 13 3y + 1 = 31 – 7y
2y = 4 y = 4 : 2 y = 2 3y + 7y = 31 – 1
 10y = 30 y = 30 : 10 y = 3
x = 13 + y x = 
 x = 
 x = 5
x = 13 + 2 x = 15 x = 
 x = 
 S = { 15, 2} S = {5, 3}
_1591023579.unknown
_1591024539.unknown
_1591026153.unknown
_1591028810.unknown
_1591029052.unknown
_1591029098.unknown
_1591029117.unknown
_1591029069.unknown
_1591028828.unknown
_1591028754.unknown
_1591028765.unknown
_1591028405.unknown
_1591028713.unknown
_1591028328.unknown
_1591026110.unknown
_1591026133.unknown
_1591026094.unknown
_1591024184.unknown
_1591024233.unknown
_1591024480.unknown
_1591024185.unknown
_1591024131.unknown
_1591024171.unknown
_1591023620.unknown
_1591023891.unknown
_1591023911.unknown
_1591023874.unknown
_1591023580.unknown
_1332697245.unknown
_1591022667.unknown
_1591023552.unknown
_1591022718.unknown
_1591023516.unknown
_1591021691.unknown
_1591021698.unknown
_1332697754.unknown
_1591020615.unknown
_1332697694.unknown
_1332696664.unknown
_1332697077.unknown
_1332697113.unknown
_1332697008.unknown
_1332696606.unknown
_1332696622.unknown
_1332696354.unknown