Question

Rozwiąż układy równań mrtodą podstawiania :
<nawiasy 2x-y=10
klamrowe> x+5y= -17

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

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

Answer 1

1)
2x-y=10
x+5y= -17

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

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

y = 2x-10
x -50 + 10x = -17

y = 2x -10
x +10x = -17 + 50

y = 2x -10
11x = 33

y = 2x -10
x = 33 : 11

y = 2x -10
x = 3

y = 2*3 -10 = 6 -10 = -4
x = 3

y = -4
x = 3

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 = -11 + 45

n = 9 - 3m
17m = 34

n = 9 -3m
m = 34 : 17

n = 9 - 3m
m = 2

n = 9 -3*2 = 9 -6 = 3
m = 2

n = 3
m = 2

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

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

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

b = 4a -2
31a = 1,5 +14

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

b = 4a -2
a = 15,5 : 31 = 0,5

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

b = 0
a = 0,5

Answer 2

<nawiasy = {
klamrowe> {

a)
{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=10+34
{x=-17-5y

{y=-4
{x=-17-5(-4)

{y=-4
{x=3

b)

{3m+n=9
{2m-5n= -11

{n=9-3m
{2m-5n=-11

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

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

{n=9-3m
{17m=34

{n=9-3m
{m=2

{n=9-6
{m=2

{n=3
{m=2

c)

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

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

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

{b=4a-2
{31a=15,5// przez 31

{b=4a-2
(a=0,5

{b=2-2
(a=0,5

(a=0,5
{b=0

Answer 3

A)
{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=44
{x=-17-5y

{y=-4
{x=-17-5*(-4)

{y=-4
{x=3

b)
{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

{n=9-3*2
{m=2

{n=3
{m=2

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

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

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

{b=-4a+2
{25a=12,5

{b=-4*0,5+2
{a=0,5

{b=0
{a=0,5