x-3y=13 and 5x+3y=2 using solving linear systems of elimination

Question

x-3y=13

5x+3y=2

Answer 1

Let x-3y=13 be ( Eq. 1 ) and 5x+3y=2 be ( Eq. 2 ). Add ( Eq. 1 ) and ( Eq. 2 ) to eliminate y, and that is:

6x = 15

x = 15 / 6 

Multiply ( Eq. 1 ) by -5 to get ( Eq. 3 ), that is:

- 5x + 15y = -65  ( 3 )

Add ( Eq. 3 ) and ( Eq. 2 ) to get y, and that is:

18y = - 63

y = - ( 63 / 18 )

Answer 2

Given equations are x-3y = 13 --------> (1)

5x+3y = 2 ---------> (2)

To eliminate the y value, add the equations (1)&(2).

x-3y = 13

5x+3y = 2

_________

6x = 15

Divide to each side by 6.

6x/6 =15/6

⇒ x = 5/2

Substitute the x value in (1).

5/2-3y = 13

-3y = 13-5/2

-3y = 21/2

Divide to each side by negitive 3.

-3y/-3 = 21/2*-3

⇒ y = -7/2