Question

Rozwiąż podane okłady równań metodą przeciwnych współczynników.
A) 3x + y = 5
2x - y = 0

B) 2x - y = 5
x + y = 4

C) -x - y = -6
-x + y = 2

D) 4x - 5y = -4
-2x + 3y = 1,1

E) -2x + y = 0
3x - 3y = 1

F) 3x - 2y = - 12
2x - 5y = - 19

Answer 1

A)3x + y = 5 3x+y=5
2x - y = 0 3×1+y=5
3x+2x+y-y=5 4+y=5/-4
5x=5/:5 y=1
x=1

b)2x - y = 5
x + y = 4
2x+x-y+y=5+4
3x=10

Answer 2

A)
( 3x + y = 5
( 2x - y = 0
__________
5x = 5 /;5
x = 1

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

( x = 1
( y = 2

B)
( 2x - y = 5
( x + y = 4
__________
3x = 9 /:3
x = 3

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

( x = 3
( y = 1

C)
( -x - y = -6
( -x + y = 2
___________
-2x = -4 /:(-2)
x = 2

-x + y = 2
-2 + y = 2
y = 2 + 2
y = 4

( x = 2
( y = 4

D)
( 4x - 5y = -4
( -2x + 3y = 1,1 /*2

( 4x - 5y = -4
( -4x + 6y = 2,2
_______________
y = -1,8

4x - 5y = -4
4x -5*(-1,8) = - 4
4x + 9 = - 4
4x = -4 - 9
4x = -13 /:4
x = -¹³/₄ = -3¼ = -3,25

( x = -3,25
( y = -1,8

E)
( -2x + y = 0 /*3
( 3x - 3y = 1

( -6x +3 = 0
( 3x - 3y = 1
___________
-3x = 1 /:(-3)
x = - ⅓

3x - 3y = 1
3*(- ⅓) - 3y = 1
-1 - 3y = 1
-3y = 1 + 1
-3y = 2 /:(-3)
y = -⅔

( x = - ⅓
( y = -⅔

F)
( 3x - 2y = -12 /*2
( 2x - 5y = -19 /*(-3)

( 6x - 4y = -24
( -6x + 15y = 57
______________
11y = 33 /:11
y = 3

3x - 2y = -12
3x - 2*3 = -12
3x - 6 = -12
3x = -12 + 6
3x = -6 /:3
x = -2

( x = -2
( y = 3