Proszę o rozwiązanie ukladów równań z góry wielkie dzięki.a)\left \{ {{\frac{1}{2}x+\frac{1}{4}y=\fr.... Question from @ucen19954

ucen19954 @ucen19954

October 2018 1 31 Report

Proszę o rozwiązanie ukladów równań z góry wielkie dzięki.

a)\left \{ {{\frac{1}{2}x+\frac{1}{4}y=\frac{1}{4}x-1} \atop- {\frac{1}{4}x+\frac{1}{2}y=\frac{1}{4}y+3}} \right.

b)\left \{ {{\frac{1}{2}(x-y)=\frac{1}{3}(x+y)} \atop {\frac{4}{5}x-\frac{1}{5}(y+3x)=-4}} \right.

c)\left \{ {{\frac{x-1}{2}+\frac{y+1}{3}=3} \atop {\frac{x+1}{3}-\frac{y-2}{6}=2}} \right.

kukur1

{1/2x + 1/4y = 1/4x - 1 /*4

{-1/4x + 1/2y = 1/4y + 3 /*4

{2x + y = x - 4

{-x + 2y = y + 12

{x + y = -4 /*(-1)

{-x+y = 12

2y = 8

y=4

x+y=-4

x+4=-4

x=-8

{x=-8

{y=4

{ 1/2(x-y) = 1/3(x+y) /*6

{4/5x - 1/5(y+3x) = -4 /*5

{ 3(x-y) = 2(x+y)

{4x-(y+3x) = -20

{3x-3y = 2x+2y

{4x-y-3x = -20

{3x-2x-3y-2y = 0

{x-y = -20

{x-5y = 0

{x-y = -20 /*(-1)

{x-5y=0

{-x+y=20

-4y=20

y=-5

x-y=-20

x+5=-20

x=-25

{x=-25

{y=-5

{(x-1)/2 + (y+1)/3=3 /*6

{(x+1)/3 - (y-2)/6 = 2 /*6

{ 3(x-1) + 2(y+1) = 18

{ 2(x+1) - (y-2) = 12

{3x - 3 + 2y+2 = 18

{2x+2 - y + 2 = 12

{3x + 2y = 19

{2x-y = 8 /*2

{3x+2y = 19

{4x-2y = 16

7x = 35 /:7

x = 5

2x-y = 8

2*5 - y = 8

10-y=8

-y=8-10

-y=-2

y=2

{x=5

{y=2

5.0

3 głosy

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5.0

3 głosy

Oceń!

a) $\left \{ {{\frac{1}{2}x+\frac{1}{4}y=\frac{1}{4}x-1\\ \\ } \atop- {\frac{1}{4}x+\frac{1}{2}y=\frac{1}{4}y+3\\ \\}} \right. \\ \\ \left \{ {{\frac{1}{2}x+\frac{1}{4}y-\frac{1}{4}x=-1} \atop- {\frac{1}{4}x+\frac{1}{2}y-\frac{1}{4}y=3}} \right.\\ \\ \left \{ {{\frac{2}{4}x+\frac{1}{4}y-\frac{1}{4}x=-1} \atop- {\frac{1}{4}x+\frac{2}{4}y-\frac{1}{4}y=3}} \right.\\ \\ \left \{ {{\frac{1}{4}x+\frac{1}{4}y=-1} \atop- {\frac{1}{4}x+\frac{1}{4}y=3}} \right.\\ \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\\$

$\frac{1}{4}y+\frac{1}{4}y=-1+3\\ \\ \frac{2:2}{4:2}y=2\\ \\ \frac{1}{2}y=2\ \ |*2\\ \\ y=4$

$\frac{1}{2}x+\frac{1}{4}*4=\frac{1}{4}x-1\\ \\ \frac{1}{2}x+1=\frac{1}{4}x-1\\ \\ \frac{1*2}{2*2}x-\frac{1}{4}x=-1-1\\ \\ \frac{2}{4}x-\frac{1}{4}x=-2\\ \\ \frac{1}{4}x=-2 \ \ \ |*4\\ x=-8$

odpowiedź:

$\left \{ {{x=4} \atop {y=-8}} \right.$

b) $></p><p> </p><p><img src=$

$\frac{1}{2}(x-(-5))=\frac{1}{3}(x+(-5))\\ \\ \frac{1}{2}x+\frac{5}{2}=\frac{1}{3}x-\frac{5}{3} \ |*6\\ \\ 3x+15=2x-10\\ \\ 3x-2x=-15-10\\ x=-25$

odpowiedź:

$\left \{ {{x=-25} \atop {y=-5}} \right.$

c) $\left \{ {{\frac{x-1}{2}+\frac{y+1}{3}=3 \ |*6} \atop {\frac{x+1}{3}-\frac{y-2}{6}=2}\ |*6} \right.\\ \\ \left \{ {{3(x-1)+2(y+1)=18 \ } \atop {2(x+1)-y-2=12}\ } \right.\\ \\ \left \{ {{3x-3+2y+2=18 \ } \atop {2x+2-(2y-2)=12}\ } \right.\\ \\ \left \{ {{3x+2y=18+1 \ } \atop {2x-2y=8}\ |*2\ } \right.\\ \\ \left \{ {{3x+2y=19 \ } \atop {4x-2y=16}\ } \right.\\ \_\_\_\_\_\_\_\_\_\_\_\_\_\_\\ 3x+4x+2y-2y=19+16\\ 7x=35 |:7\\ x=5$