Question

Rewrite the following equation in standard form.

10
9
x
+
4
5
y
=
1
5

Answer 1

To rewrite the equation given as:

\[
\frac{10}{9}x + \frac{4}{5}y = \frac{1}{5}
\]

in standard form, we want to eliminate the fractions and express it in the form \(Ax + By = C\), where \(A\), \(B\), and \(C\) are integers.

1. Start by multiplying all terms by the least common multiple (LCM) of the denominators (9, 5, and 5). The LCM of these numbers is 45.

Multiply each term by 45:

\[
45 \left(\frac{10}{9}x\right) + 45 \left(\frac{4}{5}y\right) = 45 \left(\frac{1}{5}\right)
\]

2. Simplify each term:

\[
45 \cdot \frac{10}{9}x = 5 \cdot 10x = 50x
\]

\[
45 \cdot \frac{4}{5}y = 9 \cdot 4y = 36y
\]

\[
45 \cdot \frac{1}{5} = 9
\]

3. Substitute these simplifications back into the equation:

\[
50x + 36y = 9
\]

Now, we have the equation in standard form:

\[
50x + 36y = 9
\]