Question

How do you solve the system `1/3 x - 1/12 y = -7` and `1/3 x + 1/6 y = 11`?

Answer 1

x = -3 and y = 72

Explanation:

So we are given with `2` equations

equation 1 is `1/3x - 1/12y` = -7

equation 2 is `1/3x + 1/6y` = 11

equation 1 can be written as `4x - y = -84`
(multiplied the whole equation by 12)

equation 2 can be written as `2x + y = 66`
(multiplied whole equation by 6)

now we add both the equations

==> `4x - y + 2x + y = -84 + 66`
==> `6x = -18`

==> `x = -18/6`

==> `x = -3`

now we substitute `x = -3` in any one of the equations
we will get `y = 72`

Answer 2

`x = -3 and y =72`

Explanation:

Both equations have the same `x`- coeffiecients.

Rewrite both equations:

`1/3x = 1/12y -7" "and" "1/3x= -1/6y +11`

`1/3x = 1/3x` , so equate the right sides of the equations.

`1/12y -7 = -1/6y +11" "larr` multiply by `12`

`y-84 = -2y+132`

`y +2y = 132+84`

`3y = 216`

`y = 72`

Substitute to find `x`

`1/3x = 1/12 (72)-7`

`1/3x = 6-7`

`1/3x = -1`

`x =-3`