# Question #ccc07

Dec 16, 2016

$x - 2 y + 6 = 0$

#### Explanation:

The standard form of an equation of this type is $a x + b x + c = 0$, where $x \mathmr{and} y$ are variables(not having fixed value) and $a , b \mathmr{and} c$ 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.

$y - y = \frac{1}{2} x + 3 - y$
$\frac{1}{2} x - y + 3 = 0$

Now, we have to convert $\frac{1}{2}$ 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,

${\cancel{2}}^{1} \times \frac{1}{\cancel{2}} x - 2 \times y + 2 \times 3 = 2 \times 0$
$\implies x - 2 y + 6 = 0$

This is the standard form of the equation.

Dec 16, 2016

$- 1 x + 2 y = 6$

#### Explanation:

The standard form for a linear equation is:

$A x + B y = C$ 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:

$- 2 y = - 2 \left(\frac{1}{2} x + 3\right)$

$- 2 y = - 1 x - 6$

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

$1 x - 2 y = 1 x - 1 x - 6$

$1 x - 2 y = 0 - 6$

$1 x - 2 y = - 6$