Question

resolva os sistemas formados pelas equações: a) x+y=1... 4x+7y=10 b) 3x+y=13... x-2y=2 c) 2x+y=4... 3x-y=1 d)2x+y=5... x-y=1 e) x+y=4... 3x+2y=9

Answer 1

a) {x+y=1
{4x+7y=10
x=1-y
4(1-y)+7y=10
4-4y+7y=10
-4y+7y=10-4
3y=6
y=6/3
y=2
x=1-y
x=1-2
x=-1
S={(-1, 2)}
b) {3x+y=13
{x-2y=2
x=2+2y
3(2+2y)+y=13
6+6y+y=13
6y+y=13-6
7y=7
y=7/7
y=1
x=2+2y
x=2+2.1
x=2+2
x=4
S={(4, 1)}
c) {2x+y=4
{3x-y=1
y=4-2x
3x-4-2x=1
3x-2x=1+4
x=5
y=4-2x
y=4-2.5
y=4-10
y=-6
S={(5, -6)}
d) {2x+y=5
{x-y=1
x=1+y
2(1+y)+y=5
2+2y+y=5
2y+y=5-2
3y=3
y=3/3
y=1
x=1+y
x=1+1
x=2
S={(2, 1)}
e) {x+y=4
{3x+2y=9
x=4-y
3(4-y)+2y=9
12-3y+2y=9
-3y+2y=9-12
-y=-3.(-1)
y=3
x=4-y
x=4-3
x=1
S={(1, 3)}

Answer 2

Resposta:

a) {x+y=1

{4x+7y=10

x=1-y

4(1-y)+7y=10

4-4y+7y=10

-4y+7y=10-4

3y=6

y=6/3

y=2

x=1-y

x=1-2

x=-1

S={(-1, 2)}

b) {3x+y=13

{x-2y=2

x=2+2y

3(2+2y)+y=13

6+6y+y=13

6y+y=13-6

7y=7

y=7/7

y=1

x=2+2y

x=2+2.1

x=2+2

x=4

S={(4, 1)}

c) {2x+y=4

{3x-y=1

y=4-2x

3x-4-2x=1

3x-2x=1+4

x=5

y=4-2x

y=4-2.5

y=4-10

y=-6

S={(5, -6)}

dx) {2x+y=5

{-y=1

x=1+y

2(1+y)+y=5

2+2y+y=5

2y+y=5-2

3y=3

y=3/3

y=1

x=1+y

x=1+1

x=2

S={(2, 1)}

e) {x+y=4

{3x+2y=9

x=4-y

3(4-y)+2y=9

12-3y+2y=9

-3y+2y=9-12

-y=-3.(-1)

y=3

x=4-y

x=4-3

x=1

S={(1, 3)}