Q37. - Algebra 2

Question

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

$\frac{5}{6}x+\frac{1}{15}y=\frac{3}{10}$

Step-by-Step Solution

Answer

The standard form of the given equation is $25x+2y=9$ and the value of A, B and C are $25,2\text{ and 9}$ respectively.

Step 1- Given information

A linear equation $\frac{5}{6}x+\frac{1}{15}y=\frac{3}{10}$.

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,

$\begin{array}{l}\frac{5}{6}x+\frac{1}{15}y=\frac{3}{10}\\ \Rightarrow \frac{25x+2y}{30}=\frac{3}{10}\\ \Rightarrow 25x+2y=\frac{3\times 30}{10}\\ \Rightarrow 25x+2y=9\end{array}$

The standard form of the given equation is:

$25x+2y=9$

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

So, $A=25,B=2\text{ and }C=9$

Hence, the standard form of the given equation is $25x+2y=9$ and the value of A, B and C are  $25, 2\text{ and 9 }$respectively.