Question

4. Rezolvaţi sistemele: (2x-3y=17 3x+2y=6 a) ; b) [3(2x+y)-2(x+2y-5)=20 5(x-y+2) = 4(2x-y+3)-13​

Answer 1

Răspuns:

Explicație pas cu pas:

a)

{2x-3y=17  I·2

{3x+2y=6   I·3 =>

----

{4x-6y = 34

{9x+6y = 18

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4x+9x = 34+18 =>

13x = 52 => x = 52:13 => x = 4

3·4+2y = 6 => 2y = 6-12 => y = -3

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b)

{[3(2x+y)-2(x+2y-5)=20

{5(x-y+2) = 4(2x-y+3)-13

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{6x+3y-2x-4y+10 = 20

{5x-5y+10 = 8x-4y+12-13

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{4x-y = 10

{8x-5x-4y+5y= 10+1

----

{4x-y = 10

{3x+y = 11

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7x = 21 => x = 21:7 => x = 3

y = 4x-10 => y = 4·3-10 = 12-10 => y = 2