Q33. - Algebra 2

Question

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

$33.\frac{1}{2}x+\frac{1}{2}y=6$

Step-by-Step Solution

Answer

The standard form of the given equation is $x+y=12$ and the value of A, B and C are $1,1\text{ and 12}$respectively.

Step 1- Given information

A linear equation $\frac{1}{2}x+\frac{1}{2}y=6$.

Step 2- Concept used

The Standard form of a linear equation is:

$Ax+By=C$   where, A, B and C are integers whose greatest common factor is 1.

Step 3- To find the standard form and value of A, B and C

From given information,

$\begin{array}{l}\frac{1}{2}x+\frac{1}{2}y=6\\ \Rightarrow \frac{x+y}{2}=6\\ \Rightarrow x+y=12\end{array}$

The standard form of the given equation is:

$x+y=12$

Now compare this equation by the equation $Ax+By=C$.

So, $A=1,B=1\text{ and }C=12$

Hence, the standard form of the given equation is $x+y=12$ and the value of A, B and C are $1,1\text{ and 12}$ respectively.