# How do you solve the following system of equations by elimination: > 2x=1+3y 5x+6y=16

sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted on

You need to isolate the terms that contain x and y to the left side, such that:

`{(2x - 3y = 1),(5x + 6y = 16):}`

You should eliminate the variable `y` , hence, you need to multiply the first equation by 2, such that:

`{(4x - 6y = 2),(5x + 6y = 16):}`

`9x = 18 => x = 2`

Substituting 2 for x in the first equation, yields:

`4 - 3y = 1 => -3y = 1 - 4 => -3y = -3 => y = 1`

Hence, evaluating the solution to the system of equations, using elimination, yields `x = 2` and `y = 1.`

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

The following set of equations has to be solved:

2x=1+3y ...(1)

5x+6y=16 ...(2)

(1) => 2x - 3y = 1 ...(3)

To eliminate y, add 2*(3) + (2)

=> 5x + 6y + 4x - 6y = 16 + 2

=> 9x = 18

=> x = 2

To eliminate x, add 2*(2) - 5*(3)

=> 10x + 12y - 10x + 15y = 32 - 5

=> 27y = 27

=> y = 1

The solution of the set of equations is x = 2 and y = 1