Question

Sistema lineares

a) 3 × + y = 8
4 × - y = 7

b) 2 × + y = 6
3 × + 2 y = 3

c) 3 × - 4 y = 3
- 3 × - 4 y = 5

d) 10 × + 10 y = 10
10 × - 8 y = 4

Answer 1

Sistema lineares

a)

{3 × + y = 8
{4 × - y = 7
---------------(+)
7x=15
x=15/7

3x+y=8
3*(15/7)+y=8
45/7+y=8
y=11/7


b)

{2 × + y = 6 --->*(-2)
{3 × + 2 y = 3

{-4x - 2y= -12
{3x + 2y=3
-----------------(+)
-7x= -9
7x=9
x=9/7

2x+y=6
2*9/7+y=6
18/7+y=6
y=24/7




c)

{ 3 × - 4 y = 3
{- 3 × - 4 y = 5
-------------------(+)
0+8y= 8
y=8/8
y=1

3x-4y=3
3x-4*1=3
3x=3+4
3x=7
x=7/3





d)

{10 × + 10 y = 10 *(-1)
{10 × - 8 y = 4

{-10x-10y=-10
{10x-8y=4
------------------(+)
-18y= -6
y= 6/18
y= 1/3


10x+10y=10
10x+10*1/3=10
10x+10/3=10
10x=10-10/3
x=2/3