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

hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

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

pohnpei397 | College Teacher | (Level 3) Distinguished Educator

Posted on

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

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

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)

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}.