*We may also use the substitution method.*

We are asked to solve the following system of equations:

2x - 5y = -2

3x + y = 6

We will use the substitution method.

First we will solve for y in terms of x in the second equation.

=> 3x + y = 6

=> y = -3x + 6

Now we will substitute the expression for y into the first equation and solve for x.

=> 2x - 5y = -2

=> 2x - 5(-3x + 6) = -2

=> 2x + 15x - 30 = -2

=> 17x - 30 = -2

=> 17x = 28

=> x = 28/17

Substituting the value 28/17 into the expression for y, we find

=> y = -3x + 6

=> y = -3(28/17) + 6

=> y = 18/17

**The solution for the system of equations is ( 28/17, 18/17).**

We'll solve the system using elimination method:

2x - 5y = -2 (1)

3x + y = 6 (2)

We'll multiply (1) by 3 and (2) by -2:

6x - 15y = -6 (3)

-6x - 2y = -12 (4)

We'll add (3) and (4):

6x - 15y - 6x - 2y = -6 - 12

We'll combine and eliminate like terms:

-17y = -18

We'll divide by -17:

y = 18/17

We'll substitute y in (2):

3x + y = 6

3x + 18/17 = 6

We'll subtract 18/17

3x = 6 - 18/17

3x = 84/17

x = 84/17*3

x = 28/17

The solutions of the equation are: {28/17 ; 18/17}.