Question

Poderiam me ajudar?
Resolva os sistemas:
a)7a+4b=7
2a+4b=2
b)10x+2y=6
-5x+2y=-9
c)5x+2y=22
2x+3y=11
d)2x+y=1
3x-4y=29
e)3x-2y=10
5x+4y=2

Answer 1

a)

{7a+4b=7 × (-1)
{2a+4b=2
:
:
{-7a - 4b= - 7
{2a + 4b = 2
------------------(+)
-5a = - 5 *(-1)
5a= 5
a=5/5
a=1


2a + 4b=2
2.(1) + 4b= 2
2 + 4b= 2
4b= 2-2
4b=0
b=0/4
b=0


s ( 1 , 0 )



b)

{10x+2y=6 × (-1)
{-5x+2y= -9
:
:
{ -10x - 2y = -6
{-5x + 2y =-9
--------------------(+)
-15x = - 15*(-1)
15x= 15
x=15/15
x=1

10x +2y = 6
10*(1)+2y= 6
10 + 2y = 6
2y= 6 -10
2y= - 4
y= -4/2
y= - 2


s ( 1 , -2 )







c)

{5x+2y=22
{2x+3y=11
:
:
{x=22/5 - 2/5 y
{ 2x +3y =11
:
:
2*(22/5 - 2/5y)+3y =11

44 - 4 /5 y+ 3y =11

40/5y +3y =11

8y+3y=11

11y=11

y=11/11

y=1


x=22/5 -2/5

x=4


s ( 4 , 1 )






d)

{2x+y=1 *(-4)
{3x-4y=29
:
:
{ -8x-4y= -4
{3x - 4y= 29
--'----------------
-5x=25
x= -25/5
x= -5


3x - 4y=29


3 *(-5) -4y= 29

-15 -4y =29

-4y= 29+15

-4y=44*(-1)

4y= -44

y=-44/4


y= - 11


s ( - 5 , -11 )









e)


{3x-2y=10
{5x+4y=2