Question

1 resolva os sistemas
A{2x-2y=8
{2x- y=9

B{2x-3y=10
{4x-y=-1

C{2x+3y=10
{4x -y=-1

D{x-y=4
{2x-y=9

Answer 1

A)
2x - 2y = 8
2x - y = 9

2x = 8 + 2y
x = 4 + y

2(4 +y) - y = 9
8 + 2y - y = 9
8 + y = 9
y = 9 - 8
y = 1
 
2x - 2y = 8
2x - 2(1) = 8
2x = 8 + 2
x = 5

S { x = 5, y = 1 } 

B)
2x - 3y = 10
4x - y = -1

- y = - 1 - 4x(-1)
y = 1 + 4x

2x - 3(1 + 4x) = 10
2x - 3 - 12x = 10
10x = 13
x = 13/10

2(13/10) - 3y = 10
26/10 - 3y = 10
26 - 30y = 100
-30y = 74
-y = 74/30
y = -74/30

S { x= 13/10, y = -74/30}

C)
2x + 3y = 10
4x - y = -1

-y = - 1 - 4x
y = 1 + 4x

2x + 3(1 + 4x) = 10
2x + 3 + 12x = 10
10x = 7
x = 7/10

4(7/10) - y = -1
28/10 - y = -1
28 - 10y = -10
-10y = -38
-y = -38/10(-1)
y = 19/5

S { x = 7/10, y = 19/5}

D)
x - y = 4
2x - y = 9

x = y + 4
2(y + 4) - y = 9
2y + 8 - y = 9
y = -1

x - y = 4
x + 1 = 4
x = 3

S { x = 3, y = -1}