Question

Rozwiąż układy równań:

a) a=b
2a+b=9

b) u=4v
5u-v=10

c)3r=s
3r+s=24


d) 2x-y+10
x+5y=-17

e) 3m+n=9
2m-5n=-11

f) 4a-2=b
3a+7b=1,5

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

h) 6x-3y=9
x+5y=-9,5

Answer 1

A) {a=b
{2a+b=9

{a=b
{2b+b=9

{a=b
{3b=9 |:3

{a=b
{b=3

a=3
b=3

b)
{u=4v
{5u-v=10

{u=4v
{5razy4v-v=10

{u=4v
{20v-v=10

{u=4v
{19v=10

{u=4v
{v=10:19

{u=4razy10:19
{v=10:19

{u=40:19
{v=10:19

c)
{3r=s
{3r+s=24

{3r=s
{3r+3r=24

{3r=s
{6r=24 |:6

{3r=s
{r=4

{3razy4=s
{r=4

{s=12
{r=4

Answer 2

A) a=b
2a+b=9

a=b
2b + b = 9

a=b
3b=9 /:3

a=b
b=3

a=3
b=3

b) u=4v
5u-v=10

u=4v
5*4v - v=10

u=4v
20v - v=10

u=4v
19v=10 /:19

u=4v
v = 10/19

u= 10/19 * 4 = 2 i jedna dwudziesta
v = 10/19

c)3r=s
3r+s=24

3r=s
3r + 3r=24

3r=s
6r=24 /:6

3r=s
r=4

s = 3*4 = 12
r=4

d) 2x-y+10
x+5y=-17

2x-y=-10
x=-17 - 5y

2*(-17-5y) - y=-10
x=-17 - 5y

-34-10y-y=-10
x=-17 - 5y

-11y = 24 /:(-11)
x=-17 - 5y

y= - 24/11
x= -17 - 5*(-24/11) = -17 + 10 10/11 = -6 i jeden jedynastych (1/11)


e)3m+n=9
2m-5n=-11

n = 9-3m
2m - 5(9-3m) = -11

n = 9-3m
2m - 45 + 15m = -11

n = 9-3m
17m = 34 /:17

n = 9-3m
m=2

n= 9 - 6 = 3
m=2

f) 4a-2=b
3a+7b=1,5

4a-2=b
3a + 7 (4a-2) = 1,5

4a-2=b
3a + 28a - 14=1,5

4a-2=b
31a = 15,5 /:31

4a-2=b
a = 1/2

b= 4*1/2 - 2 = 0
a=1/2

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

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

5x = 4 - 2(3-4x)
y=3 - 4x

5x = 4 -6 +8x
y=3 - 4x

-3x = -2 /:(-3)
y=3 - 4x

x = 2/3
y = 3 - 4* 2/3 = 3 - 8/3 = 3 - 2 2/3 = 1/3

h) 6x-3y=9
x+5y=-9,5

6x-3y=9
x = -9,5 - 5y

6*(-9,5 -5y) - 3y = 9
x = -9,5 - 5y

-57 - 30y -3y = 9
x = -9,5 - 5y

-33y = 66 /:(-33)
x = -9,5 - 5y

y = -2
x = -9,5 - 5*(-2) = -9,5 + 10 = 0,5

Answer 3

A) a=b
2a+b=9

a=b
3b=9 / :3

b=3
a=3

b) u=4v
5u-v=10

u=4v
5*4v-v=10

u=4v
19v=10 / :10

v=1,9
u=4*1,9

v=1,9
u=7,6

c)3r=s
3r+s=24

2s=24 / :2
s=12

12=3r / :3

s=12
r=4

d) 2x-y+10
x+5y=-17
???

e)3m+n=9
2m-5n=-11

n=9-3m
2m-5(9-3m)=-11

n=9-3m
2m-45+18m=-11

n=9-3m
20m=34 / :20
m=1,7

m=1,7
n=9-3*1,7

m=1,7
n= 3,9

f) 4a-2=b
3a+7b=1,5

3a+7(4a-2)=1,5
3a+28a-14=1,5
31a=15,5 / :31
a = 0,5

b=4*0,5-2
b=0

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

y=3-4x

5x=4-2(3-4x)
5x=4-6+16x
11x=2 / :11
x = 2/11

y=33/11-8/11 = 21/11

h) 6x-3y=9
x+5y=-9,5

x=-9,5-5y

6(-9,5-5y) - 3y=9
-57-30y-3y=9
-33y=66 / :(-33)
y=-2

x=-9,5-5*(-2)
x=-9,5+10
x = 0,5