Question

Rezolvați sistemele



{x-y=2
{2x+y=13

{x+y=2
{2x-y=1

{7x-y=9
{x+y=7

{x-3y=1
{+x-y=-9​

Answer 1

a)

{x-y=2

{2x+y=13

Se aduna ecuatiile => 3x=15 => x=5  => introducem in prima ecuatie

5-y=2 => y=3

(x,y)=(5,3)

b)

{x+y=2

{2x-y=1

Se aduna ecuatiile => 3x=3 => x=1  => introducem in prima ecuatie

1+y=2 => y=1

(x,y)=(1,1)

c)

{7x-y=9

{x+y=7

Se aduna ecuatiile => 8x=16 => x=2  => introducem in a doua ecuatie(pentru usurinta de calcul)

2+y=7 => y=5

(x,y)=(2,5)

d)

{x-3y=1

{+x-y=-9

(inmultimim prima ecuatia cu -1)

{-x+3y=-1

{+x-y=-9

Se aduna ecuatiile => 2y=-10 => y=-5  => introducem in a doua ecuatie(pentru usurinta de calcul)

x-(-5)=-9 => x+5=-9 => x=-14

(x,y)=(-14,-5)