Question

Write each equation in standard form. Identify A, B, and C.

$63. 6x=3y-9$

Short answer

The standard form of the equation is $2x-y=-3$and $A=2, B=-1, C=-3$.

Step-by-step solution

Step-1 – Apply the concept of Standard form of equation 

Any linear equation with variables xand ycan be expressed in the standard form as:

$Ax+By=C$

Where A, B, and C are all integers with greatest common factor as 1.

Step-2 – Convert the equation into standard form

Consider the given equation.

$6x=3y-9$

To convert it into standard form, subtract 3yon both sides of equation and divide whole equation by 3.

$\begin{array}{c}6x-3y=3y-9-3y\\ 6x-3y=-9\\ 2x-y=-3\end{array}$

Thus, the standard form of the equation is $2x-y=-3$.

Step-3 – Identification of A, B, and C

Comparing $2x-y=-3$with standard form $Ax+By=C$, we get

$\begin{array}{l}A=2\\ B=-1\\ C=-3\end{array}$

Hence, the standard form of the equation is $2x-y=-3$ and $A=2, B=-1, C=-3$.