Question

Zadanie 1. Rozwiąż układy równań metodą podstwaiania.

a) 2x+y=5
4x-y=10

b) x+2y= - jedna druga
3x+4y= -1

c) 2x+2y=4
8x-4y= -2

d) 5x+10y=5
8x-4y= -2

e) x-2y= -10
jedna druga y - 2 = 3

f) 2y-x = 8
4x+3y= 1

Answer 1

A) 2x+y=5
4x-y=10

y=5-2x
4x-y=10

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

y=5-2x
6x=15/:6

y=5-2x
x=2,5

y=5-2•2,5
x=2,5

y=5-5
x=2,5

x=2,5
y=0

b) x+2y= -0,5
3x+4y= -1

x=-0,5-2y
3x+4y= -1

x=-0,5-2y
-1,5-6y+4y=-1

x=-0,5-2y
-2y=0,5/:(-2)

x=-0,5-2y
y=-0,25

x=-0,5+0,5
y=-0,25

x=0
y=-0,25

Answer 2

A) 2x+y=5
4x-y=10
y=5-2x
4x-(5-2x)=10
y=5-2x
4x-5+2x=10
y=5-2x
6x=10+5
y=5-2x
6x=15/:6
y=5-2x
x=2,5
y=5-2*2,5
x=2,5
y=0
b) x+2y= -0,5
3x+4y= -1
x=-0,5-2y
3*(-0,5-2y)+4y=-1
x=-0,5 - 2y
-1,5-6y+4y=-1
x=-0,5-2y
-2y=-1+1,5
x=-0,5-2y
-2y=0,5/:(-2)
x=-0,5-2y
y=-0,25
x=-0,5 -2*(-0,25)
y=-0,25
x=-0,5 + 0,5
y=-0,25
x=0
c) 2x+2y=4
8x-4y= -2
2x=4-2y/:2
8x-4y=-2
x=2-y
8*(2-y)-4y=-2
x=2-y
16-8y-4y=-2
x=2-y
-12y=-18/(-12)
x=2-y
y=1,5
x=2-1,5
y=1,5
x=0,5
d)5x+10y=5
8x-4y= -2
5x=5-10y/:5
8x-4y=-2
x=1-2y
8*(1-2y)-4y=-2
x=1-2y
8-16y-4y=-2
x=1-2y
-20y=-10/:(-20)
x=1-2y
y=0,5
x=1-2*0,5
y=0.5
y=0
e)x-2y= -10
jedna druga y - 2 = 3
x-2y=-10
0,5y-2=3
x-2y=-10
0,5y=5/:(0,5)
x-2y=-10
y=10
x-2*10=-10
y=10
x-20=-10
y=10
x=10
f) 2y-x = 8
4x+3y= 1
-x=8-2y/:(-1)
4x+3y=1
X=-8+2Y
4*(-8+2y)+3y=1
X=-8+2Y
-32+8y+3y=1
X=-8+2Y
11y=33/:11
X=-8+2Y
y=3
X=-8+2*3
y=3
x=-8+6
y=3
x=-2

Answer 3

A) 2x+y=5
4x-y=10


y = - 2x+5
4x - (-2x+5) = 10

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

y = 2x+5
6x = 15/6

y = 2x+5
x = 5/3

y = 2*5/3+5
x = 5/3

y = 10/3
x=5/3




b) x+2y= - 1/2
3x+4y= -1


x = -2y - 1/2
3 ( - 2y - 1/2 ) + 4y = -1

x = - 2y-1/2
-6y - 1.5 + 4y = -1

x=-2y-1/2
2y = 0,5 //2

x = -2y - 1/2
y = 0.25


x = - 2*0.25 - 1/2
y = 0.25

x=0.25
y=0.25



c) 2x+2y=4
8x-4y= -2


2x = -2y + 4 // 2
8X - 4Y = -2

x = - y +2
8*(-y+2) -4y = -2

x = -y +2
-8y + 16 -4y = -2

x = -y +2
- 12y = - 14 //-12

x = -y + 2
y = 14/12

x = - 14/12 +2
y = 7/6

x = - 1 i 1/6 +2
y = 1 i 1/6

x = 5/6
y = 1 i 1/6



d) 5x+10y=5
8x-4y= -2


5x = -10y +5 //5
8x - 4y = -2


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

x = - 2y +1
- 16y +8 -4y = -2

x = -2y +1
-20y = - 10 // -20


x = -2y +1
y = 0.5

x = -2 * 0,5 +1

y = 0.5

x = -1 +1
y = 0.5

x = 0
y = 0,5



e) x-2y= -10
1/2 y - 2 = 3

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

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

y = 0,5x +5
0.25 x + 2,5 - 2 = 3

y = 0.5x +5
0.25x = 3.5 // 0 .25

y = 0.5x +5
x = 14

y = 0,5 * 14 +5
x =14

y = 12
x =14



f) 2y-x = 8
4x+3y= 1


x = - 2y +8
4x+3y = 1

x = - 2y + 8
4(-2y+8) + 3y = 1

x = -2y +8
- 8y + 32 + 3y = 1

x = -2y+8
- 5y = - 31 //-5

x = - 2y +8
y = 31/5 = 6 i 1/5

x = -2 * 6 i 1/5 + 8
y = 6 i 1/5

x = 12.4 + 8
y = 6 i 1/5

x = 20,4
y = 6.2