# Solve the system: 2x - 5y = -2 3x + y = 6 Solve for x

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### 3 Answers

2x - 5y = -2 ................(1)

3x + y = 6 ..................(2)

Let us use the elimination to solve,

We will multiply (2) by 5 and add tp (1):

2x- 5y = -2

15x + 5y = 30

==> 17x = 28

==> **x= 28/17**

3x + y = 6

==> y= 6- 3y

==> y= 6- 3*28/17

= 6- 84/17=

= 18/17

==> **y= 18/17**

Let us start by using the second equation to find for y. We do that by subtracting 3x from both sides. That gives us

y = 6 - 3x

Let us substitute that value of y in to the first equation.

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

2x - 30 + 15x = -2

Now we add the x terms together and we add 30 to both sides so as to get all the x terms on one side and the number terms on the other.

17x = 28

x = 28/17

We'll olve 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}.**