Respuesta :

mhanifa

Answer:

  • (-3, 5)

Step-by-step explanation:

Given system:

  • 3x+3y=6
  • 5x-6y=15

Simplify the first equation by dividing all terms by 3:

  • 3x/3 + 3y/3 = 6/3
  • x + y = 2
  • x = 2 - y

Substitute x into the second equation:

  • 5(2 - y) + 6y = 15
  • 10 - 5y + 6y = 15
  • y = 15 - 10
  • y = 5

Find x:

  • x = 2 - 5
  • x = -3

[tex]\\ \sf\longmapsto 3x+3y=6\dots(1)[/tex]

[tex]\\ \sf\longmapsto 5x-6y=15\dots(2)[/tex]

Multiply eq(1) by 2 and eq(2) by 1

[tex]\\ \sf\longmapsto 6x+6y=12[/tex]

[tex]\\ \sf\longmapsto 5x-6y=15[/tex]

  • Add

[tex]\\ \sf\longmapsto 11x=27[/tex]

[tex]\\ \sf\longmapsto x=\dfrac{27}{11}[/tex]

Now

Put in eq(1)

[tex]\\ \sf\longmapsto 3\dfrac{27}{11}+3y=6[/tex]

[tex]\\ \sf\longmapsto \dfrac{81}{11}+3y=6[/tex]

[tex]\\ \sf\longmapsto 3y=6-\dfrac{81}{11}[/tex]

[tex]\\ \sf\longmapsto 3y=\dfrac{66-81}{11}[/tex]

[tex]\\ \sf\longmapsto 3y=\dfrac{15}{11}[/tex]

[tex]\\ \sf\longmapsto y=\dfrac{15}{33}[/tex]

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