Q38. - Algebra 2

Question

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

$0.25x=0.1+0.2y$

Step-by-Step Solution

Answer

The standard form of the given equation is $5x-4y=2$ and the value of A, B and C are $5,-4\text{ and 2}$ respectively.

Step 1- Given information

A linear equation $0.25x=0.1+0.2y$.

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,

$\begin{array}{l}0.25x=0.1+0.2y\\ \Rightarrow \frac{25}{100}x=\frac{1}{10}+\frac{2}{10}y\\ \Rightarrow \frac{1}{4}x=\frac{1}{10}+\frac{1}{5}y\\ \Rightarrow \frac{1}{4}x-\frac{1}{5}y=\frac{1}{10}\\ \Rightarrow \frac{5x-4y}{20}=\frac{1}{10}\\ \Rightarrow 5x-4y=\frac{20}{10}\\ \Rightarrow 5x-4y=2\end{array}$

The standard form of the given equation is:

$5x-4y=2$

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

So, $A=5,B=-4\text{ and }C=2$

Hence, the standard form of the given equation is $5x-4y=2$and the value of A, B and C are $5,-4\text{ and 2}$ respectively.