Question

Rozwiąż układ równań

2x+xy+2y=-13

x-2xy+y=46

Answer 1

2x+xy+2y=-13/*2

x-2xy+y=46

 

4x+2xy+4y=-26

x-2xy+y=46

------------------+

5x+5y=20/:5

x+y=4 ⇒y=4-x

 

2x+x(4-x)+2(4-x)=-13

2x+4x-x²+8-2x+13=0

-x²+4x+21=0

Δ=16+4*21=100

x=(-4-10)/(-2)=7 v x=(-4+10)/(-2)=-3

y=4-7=-3           v y=4-(-3)=4+3=7

Odp. x=7, y=-3  lub  x=-3, y=7

Answer 2

2x+xy+2y = -13

x-2xy=y = 46

 

xy = -13-2x-2y

x-2xy+y = 46

 

x-2(-13-2x-2y)+y = 46

x+26+4x+4y+y = 46

5x+5y = 46-26

5x+5y = 20  /:5

x+y = 4  -> y = 4-x

 

x-2x(4-x)+4-x = 46

x-8x+2x²+4-x = 46

2x²-8x-42 = 0  /:2

x²-4x-21 = 0

Δ = 40+84 = 100

√Δ = 10 

x1 = (4-10)/2 = -3

x2 = (4+10)/2 = 7

 

y1 = 4-(-3) = 7

y2 = 4-7 = -3

 

{x1 = -3}

{y1 = 7}

 

{x2 = 7}

{y2 = -3}