Question

Rezolvați prin metoda substituţiei urmatoarele sisteme de ecuatii:
a. 4x+2y=2, 3x+y=0
b. -x+5y=-8, 3x-2y=-2
c. 3x-y=13, -x+5y=-9
d. 3x-2y=0, 4x-y=-5
e. 4x+5y=-12, x+3y=-10
f. 6x+y=-11, x+4y=-21​

Answer 1

Răspuns:

Explicație pas cu pas:

a) {4x+2y = 2

   {3x+y=0   => y = -3x

4x+2(-3x) = 2 => 4x-6x = 2 => -2x = 2 =>

x = 2:(-2) => x = -1

y = -3·(-1) => y = 3

b) {-x+5y=-8 => x = 5y+8

   { 3x-2y=-2

3·(5y+8)-2y = -2 =>15y+24-2y = -2 =>

13y = -26 => y = (-26):13 => y = -2

x = 5·(-2)+8 = -10+8 => x = -2

c) {3x-y=13 => y = 3x-13

   {-x+5y=-9

-x+5(3x-13) = -9

-x+15x-65 = -9

14x = 65-9 =>

14x = 56 => x = 56:14 => x = 4

y = 3·4-13 = 12-13 => y = -1

d) {3x-2y=0

   {4x-y=-5 => y = 4x+5

3x-2(4x+5) = 0 =>

3x-8x-10 = 0 => -5x = 10 => x = 10:(-5) => x = -2

y = 4(-2)+5 = -8+5 => y = -3

e) {4x+5y=-12

   {x+3y=-10 => x = -10-3y

4(-10-3y)+5y = -12 =>

-40-12y+5y = -12

-7y = 40-12 => y = 28:(-7) => y = -4

x = -10-3(-4) = -10+12 => x = 2

f) {6x+y=-11

  {x+4y=-21 => x = -21-4y

6(-21-4y)+y = -11 =>

-126-24y+y = -11 => -23y = 126-11 =>

-23y = 115 => y = 115:(-23) => y = -5

x = -21-4(-5) = -21+20 => x = -1

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