Question

Rozwiąż układy równań metodą przeciwnych współczynników:
1. 3x+2y= 13
2x+y=11

2. 5x+3y= 0
-x-2y= 7

3. 3u+2v= 2
5u+4v= 6

4. 3s+5t= -6
1,5s-2t= -3

5. 5= 3x-y
5x-2y= 7

6. x-3y= 5
y+3x= -5

Answer 1

3x+2y= 13
2x+y=11/*-2

3x+2y= 13
-4x-2y=-22
-1x=-9
x=9

2*9+y=11
18+y=11
y=-7


5x+3y= 0
-x-2y= 7/*5

5x+3y= 0
-5x-10y=35
-7y=35
y=-5

5x-15=0
x=3

3u+2v= 2/*-2
5u+4v= 6

-6u-4v=-4
5u+4v= 6

-u=2
u=-2

6+2v=2
2v=2-6
2v=-4
v=-2


3s+5t= -6
1,5s-2t= -3/*-2

3s+5t= -6
-3s+4t=6
9t=0
t=0
3s+0=-6
3s=-6
s=-2


5= 3x-y/*-2
5x-2y= 7
-6x+2y=-10
5x-2y=7
-x=-3
x=3
15-2y=7
-2y=-8
y=4


x-3y= 5/*-3
y+3x= -5
-3x+9y=-15
y+3x= -5
10y=-20
y=-2
x-2*-3=5
x+6=5
x=-1

Answer 2

3x+2y= 13
2x+y=11/*-2
3x+2y=13
-4x-2y=-22
-x=9/:-1
x=-9
3*(-9)+2y=1
x=-9
-27+2y=1
x=-9
2y=1+27
x=-9
y=28/:2
x=-9
y=14

5x+3y= 0
-x-2y= 7/*5
5x+3y=0
-5x-10y=35
-7y=35/:-7
y=-5
5x+3*(-5)=0
y=-5
5x-15=0
y=-5
5x=0+15
y=-5
x=15/:5
y=-5
x=3


3u+2v= 2 /*-2
5u+4v= 6
-6u-4v=-4
5u+4v=6
-1u=2/:-1
u=-2
3*(-2)+2v=2
u=-2
-6+2v=2
u=-2
2v=2+6
u=-2
v=8/:2
u=-2
v=4

3s+5t= -6
1,5s-2t= -3/*-2
3s+5t=-6
-3s+4t=6
9t=0/:9
t=0
3s+5*0=-6
t=0
3s+0=-6
t=0
3s=-6/:3
t=0
s=-2

5= 3x-y
5x-2y= 7
-3x+y=-5/*2
5x-2y=7
-6x+2y=-10
5x-2y=7
-x=-3/:-1
x=3
5=3*3-y
x=3
5=9-y
x=3
y=9-5
x=3
y=4

x-3y= 5
y+3x= -5/*3
x-3y=5
3y+9x=-15
10x=-10/:10
x=-1
-1-3y=5
x=-1
-3y=5+1
x=-1
y=6/:-3
x=-1
y=-2

Answer 3

3x+2y= 13
2x+y=11/* -2

3x+2y=13
-4x-2y=-26
-x=13/ * -1
x=13

3*13+2y=13
39+2y=13
2y=13-39
y= -26


5x+3y= 0
-x-2y= 7/ *5
5x+3y= 0
-5x-10y=35
-7y=35/: -7
y=5
5x+3y= 0
5x+3*5=0
5x+15=0
5x=-15/: 5
x=-3




3u+2v= 2/* -2
5u+4v= 6
-6u-4v=-4
5u+4v= 6
-u=2
u=-2
5u+4v= 6
5* -2+4v=6
-10+4v=6
4v=16/4
v=4


3s+5t= -6
1,5s-2t= -3/*2
3s+5t= -6
3s-4t=-6/* -1
3s+5t= -6
-3s+4t=6
9t=0
t=-9
3s+5t= -6
3s+5* -9=-6
3s-45=-6
3s=-6+45
s=13