Question

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

$\frac{2}{3}y-6=1-x$

Short answer

The standard form of the equation is $3x+2y=21$and localid="1647606012634" $A=1, B=2, C=6$.

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.

$\frac{2}{3}y-6=1-x$

To convert it into standard form, add x and 6on both sides of equation.

$\begin{array}{c}\frac{2}{3}y-6+x+6=1-x+x+6\\ x+\frac{2}{3}y=7\end{array}$

Now, multiply whole equation by $3$.

$\begin{array}{c}\left(3\right)\left(x+\frac{2}{3}y\right)=\left(3\right)\left(7\right)\\ 3x+2y=21\end{array}$

Thus, the standard form of the equation is $3x+2y=21$.

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

Comparing $3x+2y=21$with standard form $Ax+By=C$, we get

$\begin{array}{l}A=3\\ B=2\\ C=21\end{array}$

Hence, the standard form of the equation is $3x+2y=21$ and $A=3, B=2, C=21$.