Question

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2X + Y = 10
X + 3Y = 2

Answer 1

$\begin{cases}2x+y=10\\ x+3y=2\end{cases}\\\\\\\\ x+3y=2\to~~x=-3y+2\\\\\\\\2x+y=10\to ~~ 2(-3y+2)+y=10\to ~~-6y+4+y=10\to\\\\-6y+y=10-4\to~~ -5y=6\to ~~ \boxed{y=- ~ \frac{6}{5} }\\\\\\\\x=-3y+2\to ~~x=-3.(- ~ \dfrac{6}{5})+2\to~~ x= \dfrac{18}{5}+2\to\\\\ x=\dfrac{18+10}{5}\to~~ \boxed{x=\dfrac{28}{5}}\\\\\\\\ \Large\boxed{\boxed{S=\left\{ \dfrac{28}{5}~;~- ~ \frac{6}{5}\right\} }}$

Answer 2

2x + y = 10 
x + 3y = 2  (- 2)

  2x + y = 10
- 2x - 6y = - 4
----------------------
       - 5y = 6  (- 1)
5y = - 6
y =  - 6/5

2x + y = 10
2x + (- 6/5) = 10
2x - 6/5 = 10
2x = 10 + 6/5
10x/5 = 50/5 + 6/5
10x = 50 + 6
10x = 56
x = 56/10
x = 5,6

S = {5,6 ; - 6/5}

 
VERIFICAÇÃO:
2x + y = 10
2(5,6) - 6/5 = 10
11,2 - 6/5 = 10
56/5 - 6/5 = 10
50/5 = 10
10 = 10

x + 3y = 2
5,6 + 3(- 6/5) = 2
5,6 - 18/5 = 2
28/5 - 18/5 = 2
10/5 = 2
2 = 2