Question

How do you solve `2y = 4 – 6x` and `3y + 9x = 6`?

Answer 1

y = 2

Explanation:

`3y + 9x = 6`

Lets solve for y first

Add 3x to both sides

3y + 9x + 3y = 6 + 3y

9x = 6 + 3y

9x = 6 + 3y

x = 6 + 3y/9

using the value of x solve the other equation

`2y = 4-6* ((6+3y)/9)`

Solve for normal division that is `(6+3)/9` but differently

`(3y)/9 + 6/9` = `1/3y + 2/3`

Plug it into the equation

`2y = 4-6*1/3y + 2/3`

`2y = 4-6/18y + 12/18`

Reduce the fractions to lower terms

`2y = 4-1/3y + 2/3`

`2y =1/3y + 2/3`

Simplify

`4 -1/3y + 2/3 = 4+(-1/3y) +2/3`

`2y = 4+(-1/3y)+2/3`

`2y = -1/3y +(4+2/3)`

`2y = -1/3y + 14/3`

Add `1/3y` to both sides

`2y +1/3y = -1/3y + 14/3 + 1/3y`

`-1/3y + 1/3y = 0`

`2y +1/3y = 14/3`

`7/3y = 14/3`

`y = (14/3)/(7/3) = 2`