2-Variable Equations & Inequalities Online Practice

To solve the given system of equations using the elimination method, we have:

1. \( 0.1x + 0.3y = 0.9 \)
2. \( 0.1x - 0.3y = 0.2 \)

Let's label the equations for easier reference:

Equation 1: \( 0.1x + 0.3y = 0.9 \)
Equation 2: \( 0.1x - 0.3y = 0.2 \)

**Step 1: Eliminate one variable**

We can subtract Equation 2 from Equation 1 to eliminate \( x \):

\[
(0.1x + 0.3y) - (0.1x - 0.3y) = 0.9 - 0.2
\]

This simplifies to:

\[
0.3y + 0.3y = 0.7
\]

Combining like terms, we have:

\[
0.6y = 0.7
\]

**Step 2: Solve for \( y \)**

Now, divide both sides by 0.6:

\[
y = \frac{0.7}{0.6} = \frac{7}{6}
\]

**Step 3: Substitute back to find \( x \)**

Now we substitute \( y = \frac{7}{6} \) back into one of the original equations. We'll use Equation 1:

\[
0.1x + 0.3(\frac{7}{6}) = 0.9
\]

Calculating \( 0.3 \times \frac{7}{6} \):

\[
0.3 \times \frac{7}{6} = \frac{21}{60} = \frac{7}{20}
\]

Now substitute back:

\[
0.1x + \frac{7}{20} = 0.9
\]

Next, we convert \( 0.9 \) to a fraction:

\[
0.9 = \frac{9}{10} = \frac{18}{20}
\]

Now we have:

\[
0.1x + \frac{7}{20} = \frac{18}{20}
\]

Subtract \( \frac{7}{20} \) from both sides:

\[
0.1x = \frac{18}{20} - \frac{7}{20} = \frac{11}{20}
\]

**Step 4: Solve for \( x \)**

Now we divide by 0.1:

\[
x = \frac{11}{20} \div 0.1 = \frac{11}{20} \div \frac{1}{10} = \frac{11 \times 10}{20} = \frac{110}{20} = 5.5
\]

Now we have \( x = \frac{11}{2} \) and \( y = \frac{7}{6} \).

**Final answer:**

The solution to the system of equations is:

\[
\left( \frac{11}{2}, \frac{7}{6} \right)
\]

From the answer choices provided, it matches with:

\( \left( \frac{11}{2}, \frac{7}{6} \right) \)