Question

1){3x-5y=8. 2){23x-17y=6. 3) {x-3•[4x-5(x-y)]=79
{x+y=8 {x+2y=3. {y-4•[3y-2•(y-x)]=7. Rezolvati sistemele de ecuatii prin metoda reducerii:
Va rog mult.multumesc

Answer 1

1)
{3x-5y=8
{x+y  = 8  |·3

{3x-5y =8
{3x+3y=24 

   / -8y = -16 ⇒  y= 2

x+2=8⇒ x= 6. 

2)
{23x-17y= 6
 {  x +2y=3 |·23

{23x-17y=6
{23x+46y= 69
  /    -63y = -63⇒ y= 1
x+2= 3⇒x=y=1 

3) {x-3[4x-5(x-y)]= 79
    {y-4•[3y-2•(y-x)]=7

{x-3(4x-5x+5y)=79
{y-4(3y-2y+2x)= 7

{x-12x+15x-15y=79
{y-12y+8y-8x    = 7

{4x- 15y= 79 |·2
{-8x - 3y= 7 

{8x-30y= 158
{-8x-3y  = 7
 / -33y = 165 ⇒y= 165:33⇒ y= 5

4x- 75= 79 ⇒ 4x= 4⇒ x=1