Question

2x+3y=4
y-3x=5

3t+1n=4
5t-2n=5

6t+3₂=2
3t+2₂=15

2x+4-1=0
½x+4=2


x-6y=9
3x-2y=19


6x-3y=2
3x+2y=15

Answer 1

1.
2x+3y=4
y-3x=5

2x+3y=4
y=3x+5

2x+3(3x+5)=4
2x+9x+15=4
11x=4-15
11x=-11 /:11
x=-1

2(-1)+3y=4
-2+2y=4
2y=6/:2
y=3

2.
3t+1n=4
5t-2n=5

3t=4-1/:3
5t-2n=5
t=(4-1n)/3
5*(4-1n)/3 - 2n=5
(20-5n)/3 - 2n=5 /*3
20-5n-6n=15
-11n=15-20
-11n=-5 / (-11)
n=5/11

3.6t+3₂=2
3t+2₂=15

6t+3₂=2
2z=15-3t /:2

64+3z=2
z=(15-3t)/2

6t+3*(15-3t)/2=2
6t+(45-9t)/2=2

(12t+45-9t)/2=2 /*2
12t+45-9t=4
3t=41/:3
t=41/3

3*41/3+2z=15
41+2z=15
2z=-26 /:2
z=(-13)

4.2x+4-1=0
½x+4=2

2x=-3
½x=-2 /:1/2

x=-3/2
x=-4 jest to układ sprzeczny

5.x-6y=9
3x-2y=19

x=6y-9
3(6y-9)=6y-9
18y-27=6y-9
12y=-18
y=-18/12
y=-3/2

x=6(-3/2)-9x=9-9
x=0

spr. 0-6(-3/2)=9
0+9=9
L=P

3*0-2(-3/2)=19
0+3≠19
L≠P

6.6x-3y=2
3x+2y=15

6x-3y=2
y=(15-3x)/2

6x-3*(15-3x)/2=2
6x-(45+9x)/2=2
(12x-45+9x)/2=2 /*2
21x=49
x=49/21

3*49/21 +2y=15
7+2y=15
2y=8 /:2
y=4

Answer 2

A)
2x+3y=4
y-3x=5

3y=4-2x
3y=15+9x

4-2x=15+9x
11x=-11
x=-1
-2+3y=4
3y=6
y=2
x=-1
b)
3t+1n=4
5t-2n=5

2n=8-6t
2n=5t-5

8-6t=5t-5
13=11t
t=1 2/11
3t+n=4
3 6/11+n=4
n=5/11
t=1 2/11
c)
6t+3?=2
3t+2?=15

6t=2-3?
6t=30-4?

2-3?=30-4?
?=28
3t+28*2=15
3t+56=15
3t=-41
t=-13 2/3
?=28
d)
2x+4-1=0
1/2x+4=2

2x=-3
x=-4
x=-1.5
rownanie zle(?)
e)
x-6y=9
3x-2y=19

3x=27+18y
3x=19+2y

27+18y=19+2y
16y=-8
y=-0.5
x-6*-0.5=9
x+3=9
x=6
y=-0.5
f)
6x-3y=2
3x+2y=15

6x=2+3y
6x=30-4y

2+3y=30-4y
7y=28
y=4
3x+2*4=15
3x=7
x=2 1/3
y=4