Question

Rozwiąż układ równań algebraicznie i graficznie

[tasdad][zadanie ]\left \{ {{\frac{x+y}{2}-\frac{x-y}{4}=-1}\atop {x+y=2}}\right \left \{ {{2(x-1)+3(y-2)=5} \atop {3(x+y)-2(x-2)=7}} [/tex]

Answer 1

a) (x+y)/2 - (x-y)/4= -1   |*4

x+y=2

 

2(x+y)-(x-y)=-4

x+y=2

 

2x+2y-x+y=-4

x+y=2

 

x+3y=-4

x+y=2   |*(-1)

 

x+3y=-4

-x-y=-2

_______________

2y=-6

y=-3

 

x+3 * (-3) =-4

x-9=-4

x=5

 

x=5

y=-3

 

 

b) 2(x-1)+3 (y-2) =5

3(x+y) -2 (x-2) =7

 

2x-2+3y -6 =5

3x +3y -2x +4 =7

 

2x+3y -8=5

x+3y +4=7

 

2x+3y=13

x+3y =3    |*(-1)

 

2x+3y=13

-x-3y=-3

________________

x=10

 

10+3y=3

3y=-7

y=-2⅓

 

x=10

y=-2⅓

Answer 2

a)

(x+y)/2 - (x-y)/4= -1   |*4

x+y=2

 

 

2x+2y-x+y=-4

x+y=2

 

x+3y=-4

y=2-x

 

x=-4-3(2-x)

x=-4-6+3x

x-3x=-10

-2x=-10

x=5

 

y=2-x

y=2-5

y=-3

 

x=5

y=-3

 

 

b) 2(x-1)+3 (y-2) =5

3(x+y) -2 (x-2) =7

 

2x-2+3y -6 =5

3x +3y -2x +4 =7

 

2x+3y -8=5

x+3y +4=7

 

2x+3y=13

x+3y =3

 

2x+3y=13

x=3-3y

 

2(3-3y)+3y=13

6-6y+3y=13

-3y=13-6

-3y=7

y=-7/3

 

x=3-3y

x=3-3(-7/3)

x=3+7

x=10

 

x=10

y=-2⅓

Answer 3

1.

(x +y)/2 -(x -y)/4 = -1   I*4

x +y =2

 

2(x +y) -(x -y) = -4

x +y =2

 

2x +2y -x +y = -4

x +y = 2

 

x +3y = -4

x +y = 2     I*(-3)

 

x +3y = -4

-3x -3y = -6

----------------

-2x =-10/:(-2)

x =5

x +y =2

y = 2 -x

y = 2 -5

y = -3

 

x =5

y = -3

2.

2(x-1) +3(y -2) =5

3(x +y) -2(x -2) =7

 

2x -2 +3y -6 =5

3x +3y -2x +4 =7

 

2x +3y =13

x +3y = 3   I*(-1)

 

2x +3y =13

-x -3y = -3

------------------

x =10

3y = 3-x

3y =3 -10

3y = -7

y = -7/3

y = -2 1/3

x =10

y = -2 i1/3