Question

Rozwiąż równania .Metodą przeciwnych współczynników
a ) 2x-y=4
2x+y=4
b ) y-3x=6
y+3x=20-10-4
c) 2x+2y=3
2x-2y=4-1
d) -3x+4y = 6
-3x-4y=6

Answer 1

A ) 2x-y=4
2x+y=4 sumujemy:
_______________
4x = 8 /:2
2x-y=4

x = 2
2*2-y = 4 /-4

x = 2
y = 0




b ) y-3x=6
y+3x=20-10-4
______________
2y = 12 /:2
y+3x = 6

y = 6
y+3x = 6

x = 0
y = 6



c) 2x+2y=3
2x-2y=4-1
___________
4x = 6
2x+2y=3

x = 1,5
2*1,5+2y=3

y = 0
x = 1,5



d) -3x+4y = 6
-3x-4y=6
____________
-6x = 12 /:(-6)
-3x+4y = 6

x = -2
-3*(-2)+4y = 6

x = -2
y = 0

Answer 2

A )
{ 2x - y = 4
{ 2x + y = 4
__________
4x = 8 /:4
x = 2

2x + y = 4
2*2 + y = 4
4 + y = 4
y = 4 - 4
y = 0

{ x = 2
{ y = 0

b )
{ y - 3x = 6
{ y + 3x = 20 - 10 - 4

{ y - 3x = 6
{ y + 3x = 6
__________
2y = 12 /:2
y = 6

y + 3x = 6
6 + 3x = 6
3x = 6 - 6
3x = 0 /:3
x = 0

{ x = 0
{ y = 6

c)
{ 2x + 2y = 3
{ 2x - 2y = 4-1

{ 2x + 2y = 3
{ 2x - 2y = 3
___________
4x = 6 /:4
x = 1,5

2x + 2y = 3
2*1,5 + 2y = 3
3 + 2y = 3
2y = 3 - 3
2y = 0 /:2
y = 0

{ x = 1,5
{ y = 0

d)
{- 3x + 4y = 6
{- 3x - 4y = 6
____________
- 6x = 12 /:(- 6)
x = - 2

- 3x + 4y = 6
- 3 * (- 2) + 4y = 6
6 + 4y = 6
4y = 6 - 6
4y = 0 /:4
y = 0

{ x = - 2
{ y = 0