Question

Question #ccc07

Answer 1

`x-2y+6=0`

Explanation:

The standard form of an equation of this type is `ax+bx+c=0`, where `x and y` are variables(not having fixed value) and `a, b and c` are integers(-3,-2,-1,0,1,2,3...).
But, in this question, we need to take `y` to the other side in order to leave only 0 on that side.
To do this, subtract `y` from both sides. This does not affect the equation.

`y-y=1/2x+3-y`
`1/2x-y+3=0`

Now, we have to convert `1/2` to an integer, and to do this we multiply it by 2. For the equation to remain unaffected, we have to multiply all terms with 2. So,

`cancel(2)^1xx1/(cancel(2))x-2xxy+2xx3=2xx0`
`=>x-2y+6=0`

This is the standard form of the equation.

Answer 2

`-1x + 2y = 6`

Explanation:

The standard form for a linear equation is:

`Ax + By = C` where `A`, `B` and `C` are integers.

Therefore, we must multiply each side of the given equation by `-2` to eliminate the fraction and keep the equation balanced:

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

`-2y = -1x - 6`

Now we can isolate the `x` and `y` terms on one side of the equation:

`1x - 2y = 1x - 1x - 6`

`1x - 2y = 0 - 6`

`1x - 2y = -6`