To solve the given system of equations using the elimination method, we start with the following equations:
- \( 0.1x + 0.3y = 0.9 \) (Equation 1)
- \( 0.1x - 0.3y = 0.2 \) (Equation 2)
To eliminate \( y \), we can add the two equations together:
\[ (0.1x + 0.3y) + (0.1x - 0.3y) = 0.9 + 0.2 \]
This simplifies to:
\[ 0.2x = 1.1 \]
Next, we solve for \( x \):
\[ x = \frac{1.1}{0.2} = 5.5 \]
Now, substituting \( x = 5.5 \) back into one of the original equations to solve for \( y \). We can use Equation 1:
\[ 0.1(5.5) + 0.3y = 0.9 \]
Calculate \( 0.1(5.5) \):
\[ 0.55 + 0.3y = 0.9 \]
Subtract \( 0.55 \) from both sides:
\[ 0.3y = 0.9 - 0.55 \] \[ 0.3y = 0.35 \]
Now, solve for \( y \):
\[ y = \frac{0.35}{0.3} = \frac{35}{30} = \frac{7}{6} \]
Thus, the solution to the system of equations is:
\[ (x, y) = \left(5.5, \frac{7}{6}\right) = \left(\frac{11}{2}, \frac{7}{6}\right) \]
Considering the response options, the correct one matches:
\[ \left( \frac{11}{2}, \frac{7}{6} \right) \]