# How do you write 5/6x+1/10y=3/10 in standard form and what is A, B, C?

Aug 10, 2017

See a 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

We can multiply each side of the equation by $\textcolor{red}{30}$ to eliminate the fractions and ensure the coefficients are integers while keeping the equation balanced:

$\textcolor{red}{30} \left(\frac{5}{6} x + \frac{1}{10} y\right) = \textcolor{red}{30} \times \frac{3}{10}$

$\left(\textcolor{red}{30} \times \frac{5}{6} x\right) + \left(\textcolor{red}{30} \times \frac{1}{10} y\right) = \frac{90}{10}$

$\frac{150 x}{6} + \frac{30 y}{10} = 9$

$\textcolor{red}{25} x + \textcolor{b l u e}{3} y = \textcolor{g r e e n}{9}$

$\textcolor{red}{A = 25}$

$\textcolor{b l u e}{B = 3}$

$\textcolor{g r e e n}{C = 9}$