# How do you write 0.25x=0.1+0.2y in standard form and what is A, B, C?

Mar 31, 2017

See the solution process below:

#### Explanation:

The standard form of a linear equation is: $\textcolor{red}{A} x + \textcolor{b l u e}{B} y = \textcolor{g r e e n}{C}$

Where, if at all possible, $\textcolor{red}{A}$, $\textcolor{b l u e}{B}$, and $\textcolor{g r e e n}{C}$are integers, and A is non-negative, and, A, B, and C have no common factors other than 1

First, subtract $\textcolor{red}{0.2 y}$ from each side of the equation so the $x$ and $y$ terms are on the left side of the equation as required by the Standard Form while keeping the equation balanced:

$0.25 x - \textcolor{red}{0.2 y} = 0.1 + 0.2 y - \textcolor{red}{0.2 y}$

$0.25 x - 0.2 y = 0.1 + 0$

$0.25 x - 0.2 y = 0.1$

Next, multiply each side of the equation by $\textcolor{red}{20}$ to eliminate the decimals and to make all of the coefficients integers while keeping the equation balanced:

$\textcolor{red}{20} \left(0.25 x - 0.2 y\right) = \textcolor{red}{20} \times 0.1$

$\left(\textcolor{red}{20} \times 0.25 x\right) - \left(\textcolor{red}{20} \times 0.2 y\right) = 2$

$\textcolor{red}{5} x - \textcolor{b l u e}{4} y = \textcolor{g r e e n}{2}$

$A = \textcolor{red}{5}$

$B = \textcolor{b l u e}{4}$

$C = \textcolor{g r e e n}{2}$